I don't allow just any old feat from any book. If it is outside the core, the player has to run it by me.
I tend to award XP at "rest times" as well, and players can generally take whatever they're interested in that passes muster. I assume that the character has been quietly working on the abilities in the background. Same goes for stat raises, skill choices, and spell choices.
I generally ask that players let me know ahead of time if they are going to do radically different multiclassing - a fighter that has never shown any interest in spellcasting ought to talk to me before taking a level of sorcerer. Not that I'm likely to disallow it, but for such large shifts, I want to know what's going through their heads, so I can better design my adventures to their desires.