I would assume that this is supposed to be “treat the hardness of anything the brawler unarmed-strikes as being lower by the number of times this FCB has been selected.” This is not particularly clear, but it’s the only reading that seems sensible. Permanently reducing the hardness of an object every time the brawler hits it is just unreasonable, and the lack of duration makes no other duration likely.

“Any object” means any object. Nothing says it doesn’t work on magical items, so it does.

Do note that magical items often have vastly higher Hardness than mundane items, so you’ll need a larger benefit here to really get anywhere with them.