A walkthrough in text form showing the direct path, some additional information and all the achievements to get. If there are any mistakes or if something is unclear please let me know about it.
Thanks to Lugum for his walkthrough, it helped a lot as a nice foundation.

Whenever I say 'the item' in the walkthrough I'm always referring to an item in your inventory, otherwise I'm referring to something in the scene.

I've played the game with the English translation and I've written everything in this walkthrough in the same way as it is in the game, you'll encounter some typos and untranslated texts.

For the people who are stuck somewhere but prefer to try to figure out the 2 bigger puzzles on their own (the "Alarm keypad" and "Flower lady" puzzles) I've put them in spoilers with hints and of course the solution :)

Tips:
- Hold Spacebar (or Esc but then you may bring up the in-game menu) to skip through conversations faster.
- Rightclicking something will always perform the 'Look at' command.
- Rightclicking someone will always perform the 'Talk to' command.
- To make the game windowed (and to go back to fullscreen) press Alt + Enter.

Look at the item "Lanor's communication device".
Click on "open/close". (if you instead click on "delete" then you can also press the required buttons on the left side without them being visible and the device will be activated as well :) )
Select "I - Introduction: Princess, representative of the galactic council" (second button).
Select "II - Performance: Princess capture, princess in danger" (third button). (after pressing the button Lanor says "Princess captured, princess in danger", it's a typo in the third button text)
Select "III - General Greene: Possible treason by Terrans, alert the rebellion" (first button).
Give the item "Lanor's communication device" to "Stellar Armada soldier" and to "General Greene". (Achievement: Sharing with the enemy)
Use the item "Lanor's communication device" with "Abandoned drain". (Achievement: Message send)

Open "Cash register".
Look at "Student travel coupons". (Achievement: Student of life)
Pick up "Student travel coupons".
Look at "Banned from the store list". (Achievement: Coffee Buyers)
Look at "Comic Books" to get the item "Screwdriver".
Use the item "Screwdriver" with "Maneki Buta" to get the item "Key".
Use the item "Key" with "Main door".
Open "Stockroom door".

Look at "5 1/4 floppy disk". (Achievement: Ups, that's not good)
Pick up "Loose piece of wallpaper" (underneath the "Alarm keypad").
Open "Bathroom door".

Pick up "Wooden stick".
Pick up "Plastic bucket" to get the item "Rubber cup".
Use the item "Piece of paper" with the item "Rubber cup" to get the item "Rubber cup with paper".
Use the item "Wooden stick" with the item "Rubber cup with paper" to get the item "Plunger".
Look at the item "Plunger". (Achievement: This is not a plunger)
Use the item "Plunger" with "Sink".
Open "Stockroom door".

In the conversation with "Lanor's communication device" select the following options in order:

• 3. How did this device get here?
  
• 3. What can I do to help you?
  
• 2. Lanor I swear I'll find you ...

Use "Alarm keypad".

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To figure out the "Alarm keypad" code:
Hint 1: When viewing the keypad there's the word "robots" written below it.
Hint 2: Check the robots in the Store.
Hint 3: Look at and take note of a date and a number from each robot.
Solution: Each robot in the Store mentions a date and a number. Put the 4 robots in the order from the oldest date to the newest date and then their numbers will form the code.

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Press 2152. (Achievement: Beyond the demo)

Open "Trash bags". (this must be done to unlock the achievement "Garbage colector" later on)
Open "Fence door".

Pick up "Bush" (you'll get the item "Riddle").
Look at "Writing on the wall" (at Narciso's place). (Achievement: Narciso's count)

In the conversation with "David" select the following options in order:

• 1. What's behind the curtain?
  
• 2. Did you develop the system?
  
• 3. See you!

Pick up "Black ink".
Pick up "Strange card".

Pick up "Trash can". (Achievement: Garbage colector)

Pick up "Lost and found box" to get the item "Dental retainers".

Use the "Bus stop" and go to the "Wings Arcade (Marty's)" at the bottom of the city (when you arrive there you'll get the item "Bus ticket").

Talk to "Strange kid".

Talk to "Kids in disguise" and select the following options in order:

• 1. What are you doing here and why are you dressed up like that?
  
• 1. And what could you give me in return if I get you that movie?
  
• 1. I'll see what I can do

Talk to "Carl Docto" and select the following options in order:

• 3. I want to rent a movie
  
• 1. iTerminator 2: Judgment Day!
  
• 5. I'd better give it some more thought
  
• 4. See you soon!

Use the item "Black ink" with "Water tank" to get the item "Diluted black ink".

In the conversation with "Emma" select the following options in order:

• 1. I've just come from the Arcade and I have important news!
  
• 1. Your 'little brother' bet my friend Marty that he would get him a date with you!

Pick up "Baby shampoo" (it's on the counter in front of "Emma").
Pick up "Toy mouse".
Look at "Doll". (Achievement: Voodoo Ritual)

Talk to "Strange girl" and select the following options in order:

• 1. What happened with this Max guy you mention?
  
• 2. Are those donuts?
  
• 2. Can I take a donut? (you'll get the item "Donuts")
  
• 3. Sorry, I have to go!

Look at "Grafitti". (this must be done to unlock the correct option for the first question from "Officer Jeff" later on in the game)
Pick up "A pair of pliers".
Use the item "A pair of pliers" with the item "Dental retainers" to get the item "Wire".
Use the item "Wire" with the item "Broken toy mouse" to get the item "Ratón de juguete reparad" (Repaired toy mouse).

Talk to "Claire" and select the following options in order:

• 1. Are you going to drink your soda?
  
• 5. See you soon

Talk to "Customer" and select the following options in order:

• 1. Do you know where I can find a guy named Data?
  
• 2. I hear you're a GREAT programmer
  
• 1. I'm Diego and I wanted to know if you can change my account status at the Video Show Club
  
• 1. In fact, I've already finished it ...

Pick up "Coffee cups" to get the item "Coffee cup".
Use the item "Diluted black ink" with the item "Coffee cup" to get the item "Cup with shampoo". (it seems the game actually expects you to first use the "Baby shampoo" instead of the ink :) )
Use the item "Baby shampoo" with the item "Cup with shampoo" to get the item "Black dye".
Look below Data's computer and take note of which color the "Network cable" is (you can hover over it to identify the cable).
Use the item "A pair of pliers" with "Network cables" (above the "Coffee machine").
Click on the wire matching the color of the "Network cable" below Data's computer.
Pick up "Soda".

Use the "Bus stop" and go to the "West Cemetery" on the left side of the city.

Talk to "Flower lady" and answer her question correctly.

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To solve the "Flower lady" puzzle:
Hint 1: Look at the item "Riddle" to get hints on what to do.
Hint 2: The yellow (Northern) building holds the Questions and the blue (Southern) building holds the Replies.
Hint 3: The Reply's position is opposite/mirrored compared to the Question's position.
Solution: The item "Riddle" says: "The last one will always cross with the first one". If the Question is on side A at the 6th position (counting from top to bottom), then the Reply is on side B at the 1st position (6th position when you count from bottom to top). If the Question is on side B at the 4th position (counting from top to bottom), then the Reply is on side A at the 3rd position (4th position when you count from bottom to top).

I can also explain a bit of a different way to solve it. Forget about the intercoms having sides A and B, view the intercoms as a whole. In the intercom of the yellow building the top-left position has the name "P.FROMTOP" and the bottom-right position has the name "L.UNDERBOTTOM". Then count from top to bottom. Count from the top-left downwards and continue counting from the top-right downwards until you hit the required Question.
To get the Reply in the blue building you then need to do it in reverse because the bottom-right position has the name "J.R.TOPPER" and the top-left position has the name "M.BOTTOMLY", so then you need to start counting from the bottom-right upwards and continue counting from the bottom-left upwards the same amount you needed to get to the Question position.

I hope this all makes sense :)

Questions (these are located in the yellow "Northern Building"):

A: B: All that glitters ... Don't count your chickens ... A picture is worth ... When in Rome ... Beggars can't ... A journey of a thousand miles ... A bird in the hand ... Too many cooks ... An apple a day ... Two wrongs ... Better safe ... When there's smoke ...

Replies (these are located in the blue "Southern Building"):

A: B: Is not gold! Before they hatch! A thousand words! Do as the Romans do! Be choosers! Begins with a single step! Is worth two in the bush! Spoil the broth! Keeps the doctor away! Don't make a right! Than sorry! There's fire!

Answers (the Questions are in alphabetical order):

A bird in the hand ... 9. Begins with a single step! A journey of a thousand miles ... 4. Is worth two in the bush! A picture is worth ... 11. Don't make a right! All that glitters ... 12. There's fire! An apple a day ... 8. Do as the Romans do! Beggars can't ... 10. Spoil the broth! Better safe ... 7. Before they hatch! Don't count your chickens ... 6. Than sorry! Too many cooks ... 3. Be choosers! Two wrongs ... 2. A thousand words! When in Rome ... 5. Keeps the doctor away! When there's smoke ... 1. Is not gold!

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Use the "Bus stop" and click on "West Cemetery" again.
Pick up "Red rose".
Use the item "Black dye" with the item "Red rose" to get the item "Black rose".
Use the "Bus stop" and go to the "Police station" at the top of the city.

Give the item "Bus ticket" to "Narciso" to get the item "Newspaper".
Look at the item "Newspaper". (this must be done to unlock the correct option for the third question from "Officer Jeff" later on in the game)

Use the item "Soda" with "Padlock".
Open "Electric board".
Pick up "Motor oil".

In the conversation with "Police officer" select the following options in order:

• 2. I want coffee!!!
  
• 3. What does that lever over there do?
  
• 4. Nothing for now

Use the item "Motor oil" with "Lever".
Use "Lever".
Give the item "Donuts" to "Police officer".
Go back into the "Police Station".
Pick up "Evidence bag" to get the item "Red spray paint".
Look at "Lockers". (Achievement: Book worm)

Use the "Bus stop" and go to the "Wings Arcade (Marty's)" at the bottom of the city.

Use the item "Red spray paint" with "Wall" (it's on the right side of "Max Martínez").
Use the "Bus stop" and go to the "Police station" at the top of the city.

Talk to "Rudy" and select the following options in order:

• 1. I want to report a crime!
  
• 1. But I have great news regarding the case you were investigating!

Use the "Bus stop" and go to the "Wings Arcade (Marty's)" at the bottom of the city.

From the conversation with "Lucy" you'll get the item "Cassette".
Look at the item "Cassette". (this must be done to unlock the correct option for the second question from "Officer Jeff" later on in the game)
Pick up "Tools".

Give the item "Pirate's tools" to "Pirate".
Give the item "Tarjeta del Video Show C" (Video Show Club Card) to "Pirate".

Give the item "Altered card" to "Data".

Talk to "Carl Docto".

Use the "Bus stop" and go to the "Police station" at the top of the city.

Open "Televic door".

Talk to "Rudy" and select the following options in order:

• 1. How about lending me that master key?
  
• 2. You're welcome!

Pick up "Poster".
Look at the item "Poster". (this must be done to unlock the correct option for the fourth question from "Officer Jeff" in the next step)

Talk to "Officer Jeff" and select the following options in order:

• 2. What if I told you I'm a Punk Rock fan?
  
• 1. 1989! (this option will be unlocked after looking at the "Grafitti" in the "Basketball court")
  
• 1. FleshDance! (this option will be unlocked after looking at the item "Cassette")
  
• 1. Three times! (this option will be unlocked after looking at the item "Newspaper")
  
• 1. Two! (this option will be unlocked after looking at the item "Poster") (Achievement: Punk Rock fan)

Go to "Path to the hill" on the left side of the street just past "Officer Jeff".

Use the item "Ratón de juguete reparad" (Repaired toy mouse) with "Stellar Armada captain". (Achievement: War elephant)
Pick up "Police master key".
Go to "Exit" on the left side of the screen.

Use the item "Master key" with "Televic door".

Open "Lab door".
Pick up "Backup tape".

Use the "Bus stop" and go to the "Wings Arcade (Marty's)" at the bottom of the city.

Talk to "Carl Docto" to get the item "Terminator 2 VHS".
Talk to "Kids in disguise" and select the following option:

• 1. Yes, I have it here! (you'll get the item "Cupón para milkshake gra" (Coupon for free milkshake))

Use the "Bus stop" and go to the "Police station" at the top of the city.

Give the item "Cupón para milkshake gra" (Coupon for free milkshake) to "Cashier" to get the item "Milkshake".

Use the "Bus stop" and go to the "Wings Arcade (Marty's)" at the bottom of the city.

Talk to "Strange kid" and select the following options in order:

• 1. I need to prove to the kid's sister that this bet is real, any ideas?
  
• 1. Can I borrow the brochure?

Give the item "Milkshake" to "Strange kid".
Give the item "Black rose" to "Strange kid" to get the item "Event brochure".

Give the item "Event brochure" to "Emma".

(when you go into the Wings Arcade the end sequence will start and you can't return anymore!)
In the conversation with "Marty" select the following option to finish the game:

• 1. I left it in Pirulín Pirulero ...