Ralph can gain stats through various means: the restaurant, stat-up items, and training while doing Challenge Tower.
These stat boosts have no real limit and can take him up to maximum stats: 999,999 HP, and 99,999 everything else.

Since the girls get stats from leveling, they are limited in how many stat gains they can get.
Every point they gain is tracked, and they can't gain any more than 1,000 extra points in a stat (for HP, it's 10,000). Extra points can be checked (and adjusted) from the fireplace after beating the first Dark Lord. Thus, the max stats for girls are what her Level 999 base stats are, plus 1,000/10,000.

There are plot scenes that play after your first expedition and after first beating each dungeon.
Plot scenes take precedent over everything else. If there are none to play, there's a 30% chance it'll pick a random return scene.
This 30% chance becomes a guarantee if you hold Shift - it does the check after the "girls' contributions" part is complete
If you have the girl(s) for the random scene and have not seen it, it will play; otherwise, it will reroll up to 90 times.

Are you sure?
Holding Down after choosing New Game will skip the intro.
Holding Shift when leaving the bar will warp you to House Park, and vice versa.
Holding Shift when using a capsule machine will let you get three capsules at once.
Holding Shift after the "girl contributions" part of returning to the village will improve the odds of a return event appearing.
After beating Part 4, holding Shift when talking to a girl in the pub will make her challenge you. (It's 1 in 15 otherwise.)

An endless supply of EXPointless accessories, which make people get 0 EXP, are hidden in the bookcase in the pub.
After beating Part 1, the fireplace in the pub will let you reduce stats and village EXP.
An old lady who randomly appears as a village NPC gives out Healer Tomes; Healer is a full-party healing spell.
Walkmaster, who randomly appears as a village NPC, pays 1 G for every step you've taken.
After beating Part 4, dungeon bosses on the first continent have a 50-50 chance of transforming into secret bosses.
The Otherworld, Monster House, and Challenge Tower can all be opened early by checking the sign/rocks 10 times.

Oc-Ock
Fight him and win for Dungeon Pillar type furniture (8 total).

Sister
Keep donating to get Statue furniture at milestones.

Roshamboy
You get random furniture (13 total) for winning.
The number of times he jumps shows his hand: 1 for Rock, 2 for Paper, 3 for Scissors.

Merchant
Always sells two random standard chest items.

Adventurer
When you first meet him, you give him an investment for his next adventure.
Next time you meet, he'll repay you based on your last investment.
Total investment helps effects; the true value used for calculations is LastInvestment + Total/50.
Repayment can be as many as 10 items, selected at random from three choices.
When an item is picked, it "uses up" some investment, and it stops when it gets too low or hits 10 items.

Magician
Give her 10,000 of Ralph's EXP for a random selection of furniture

Pressure Lady
Either gives Ralph 150 max HP and heals him, or takes 100 max HP nad puts him near death. It's a straight 50-50 chance.
If the latter happens, she also gives you a small selection of random furniture

Mash Gramps
Mash the button. If you get over 20, you get random furniture (9 total). You get 100 village EXP for each hit.

Moody Girl
Randomly has one of four moods:
1. Average. Nothing happens.
2. Really good. Random furniture (7 total): a teddy bear, rabbit, or presents.
3. Foul mood. Ralph takes 10,000 damage.
4. Gloomy. She steals friom you 5,000 G.

http://vgperson.com/games/heroanddaughter.htm