ATc 3b bb/bu

I would just shove your never in terrible shape,you could just call the raise but if the turn bricks it leaves us in an awkward spot.Besides you might as well take advantage of any fold equity as well.

Preflop 3bet is ok. I usually prefer doing it with the strongest aces (AK-AQ) or the very weak ones (A5s-A2s) though.
Depends a bit on how BB plays too.
Flop is not a mandatory cbet imo, but if I'd bet I would bet more than 1/2 in this spot. Board texture doesn't allow us to cbet range small and we are OOP. Check is ok too, do a mix of both.

As I've said in a previous post (a long time ago probably) he shouldn't be raising cbets in 3bet pot when IP. The reason is that SPR is already smaller in 3bet pots and he can easily get all-in in 3 streets. Besides that, he only strengthens your range by doing so.

I'd say 3bet is the play here taking into account we have 2 overs, the nutflush-draw and a gutshot str8-draw too. It's just too much equity.
Don't expect to be ahead when called though. It will usually be a high variance play. You can balance your bluffs with 98s, 75s, 66, 88, 99, TT, JJ.
If you call OTF, turn pot will be 17.97$ and the effective stack 14.25$ (his stack). You could also blow up your equity when it bricks as Reds said. About fold equity, I don't think you have any to be honest, which is the bigger downside of the flop 3bet.

I cannot really just raise, I should shove and I think, that is best OOP. The think is, that I don't really like to gamble with the fish, that probably never fold there:(. I t isn't that bad to just call and give up if I don't hit.

You likely have 13 clean outs blocking T7 and the Ace and Ten will be live some of the time.So with $14.25 left to call on a bricked turn you probably still have to call off on the turn given your equity and those odds.So it's probably better to just shove the flop and villain is playing less than full stacked so probably isn't the best of players.