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If I'm wrong about that being what you're looking for, then I would appreciate it if you could clarify what you are trying to find out.
Yes, that is the base crit rate that gets modified by Sharp Student/Apt Pupil.
Yes it is, basic attack with no modifiers and equal luck is, in fact, 3%.
If a skill, given 0 luck and no modifiers, has 22% crit rate, then that would mean Skill Crit is 22.
Rebellion and Revolution are additive like the crit rate passives. Apt Pupil and Sharp Student are the only parts (beyond the base crit rate) that are used as multipliers.
I get the impression that a lot of your questions stem from not being sure if the game works with decimals or whole numbers. If that impression is correct, then I feel I should clarify that the game works with whole numbers behind the scenes. Internally, if something reaches 44%, it's represented as "44" and not "0.44". As such, if a formula for probability produces "44", that means "44%" and not "4400%".
Is (ALuck + 50)/(DLuck + 50) × Skill Crit the base crit rate that gets modified by sharp student/apt pupil?
Is the result of the formula your crit rate in percent? E.g. basic attack with no modifiers and equal luck is 3% crit chance.
For a skill with, say, a 22% crit chance, does this mean Skill Crit = 22?
Do revolution and rebellion apply additively like the crit rate passives or would rebellion make the formula (ALuck + 50)/(Dluck + 50) × (Skill Crit + 7)?