[RPG] What are class skills in Pathfinder

For Skills when you multiclass all your skills immediately get the +3 class bonus provided you have at least one one rank in them.

Thus for your example:

Bob the fighter has 1 rank in acrobatics, and no stat bonus.

Bob gets +1 bonus.

Bob levels and takes 1 level in rogue. Bob now get +3 to acrobatics as acrobatics is a class skill for rogues, even though he bought this rank in acrobatics when he was a fighter. Where the rank came from is irrelevant, now Bob is a rogue it's a class skill for him.

Bob now has +4 bonus.

Like Craft, Knowledge, and Profession, Perform is actually a number of separate skills. You could have several Perform skills, each with its own ranks.

There is no need to multiclass. If you want Perform(Dance) and Perform(Oratory) you spend skill points for each seperately like a new skill. Same class can have both. This applies to all other sub categoried skills like knowledge or craft.