An ass (or donkey), 驴子, is a barn animal which is quite stupid. Calling someone an ass is like calling him very stupid!

Depends on the context in which it is used: ass = 讨厌 You are an ass! (你很讨厌！) pain in the ass = 难缠 You are such a pain in the ass! (你很难缠！) dumb ass = 笨蛋

I take it as depending on if there is a particle or not. For "an ass", you are saying someone is as stupid and stubborn as a donkey. For simply "someone is ass", you're saying that they are as pleasing and appealing as their own behind. In both contexts it's a negative meaning (imagine the ass/arse is fat, hairy and putrid).