In Pathfinder do class skill bonuses count as ranks, especially for the purpose of prestige classing, or are they a generic bonus?
If they are a bonus, how should I adjust the required ranks for prestige classes and feats when converting from D&D3?
No, they do not.
Skill ranks refer only to the number of well, ranks that you've put into the skill.
I can't find an exact reference to back that up, but they make a big deal when referring to ranks vs bonuses:
Since you can only have a number of Ranks in a given skill equal to your level, that means that a minimum number of ranks is effectively a level requirement.
So, when for example you have an Assassin who has a requirement of minimum 5 ranks in Stealth, you must be at least 6th level before even being able to become an assassin.
You're doing conversions! This free PDF will cover most of what you need to do: http://paizo.com/pathfinderRPG/v5748btpy89m6 (You do need a Paizo account to download it, but that too is free).
From the Prestige Classes section in the conversion guide:
No, they don't.
But if you're making a conversion, using the standard method of requiring 3 less ranks than it would on 3.x could result in awkward conversions.
Several 3.x prestige classes work on the assumption that you're purchasing some cross-class skills. That's mostly the case of "8 ranks of this plus 4 ranks of this, this and that".
Personally, I'd rule that you need a score of (3.x ranks needed) between ranks and the +3 bonus for putting ranks in a class skill.
No. Ranks are raw skill. All other bonuses are just that, bonuses, and added after the fact. Anything that specifies skill rank as a requirement means the raw skill rate, not the adjusted one.