Disclaimer: fish and first-time poster here. Please correct me where I do things wrong, whether it be playing or formatting.

Live 0.1/0.1 fishy and loose home game. First session with villain, but he is the best player by far at the table, playing loose aggressively, has good image and respected by everyone.

Preflop:
2 limpers. Villain in the Hijack raises to 6BB. CO calls. Hero on the button squeezes to 25BB with J T. 2 folds. villain calls. CO folds. Around 200BB effective behind.

Flop: K J 7.
Villain donks 25BB. Hero raises to 70BB. Villain calls.

Turn: 9
Villain bets 50BB. Hero folds. Villain shows AK

On the flop, I put him on KJ, KQ, bottom set and maybe middle set, flush draws, high and straight draws, even some air hands as he has reasons to think he can run over the table, with the majority of his range being bluffs/semi bluffs.

Was I wrong to excluded AK from his calling range? Should I have called the flop and c/f the turn? On the turn should I have shoved with my gut shot? Also considering him holding AK, why did he not shove on the flop but comes out betting on the turn that didn't improve his hand and unlikely to have improved mine?

live low stakes NL is probably where your supposed to post this

In the hand I probably call preflop with this hand as I'm happy to go multiway with it.

As played on the flop I would just call as I see no reason to raise here.

I probably would have called flop and folded turn.

Don't think shoving with a gutshot is wise as it doesn't give you much equity in the hand.

goodluck

Overplayed hand pre and otf. Excluding AK 200bb deep is wrong even though it does not change much the decision.
Ott shoving makes some sense as your hand blocks JJ set and has a weak draw. But I dont think you must look for such bluffs in an easy home game.
E. As for your question why he did not shove flop. He has no reason to do it, his hand has showdown value and is really safe with nut FD, TP and TopKicker. I dont think his donkbet are best strategy, maybe it is a sign he is unsure what to do, possible read on him.