Yes AC is a simulation game, quite a few people refer to it as an RPG, but it isn't, It's probably the only Do Nothing All Day game in the world, not that it isn't fun, it is, but it's very casual and is nothing like an RPG.
Nah, it lacks the traditional elements of an RPG like fighting monsters, world exploration (well, you've got the city but that's about it XD), leveling up, etc.
I'd definitely stick it in the simulation category. It's such a cute game, though! c: