nice hand history and decent thought processes you provided - this makes it a lot more fun to launch discussion.

So I'm not super convinced abot many things as well so treat it as a discussion opener.

1) Flop: Depending on that structure which is not blasting together with your 3 betting range I think this is a flop where you will have a comparatively high checking frequency. In a single raised pot in these cases I would select a bigger sizing (1/2 - 2/3 as you mentioned). However this is a 3bet pot and I'm not sure how bad it is to stick to the 1/3 pot sizing. But if you choose bigger sizings sometimes I suspect this is a board where it would fit well.

I'm not sure if a check also works good on this board but I guess a bet is fine.The best thing about betting is that if he just calls he will check again almost always on the turn and we can just check behind to realize our equity.

2) That having said I'm not sure if I like betting the turn. We don't fold out any better hands. We do get called by his weaker flush draws which we dominate and which is quite attractive. But considering value hands we don't get called very likely by holdings like pocket pairs wrapping around the medium cards (66, 77, 88, TT, JJ). We might get some calls with TT and JJ but probably not always? And of these we can get this value on the river as well. So I would just take the easy way here because the danger is we bloat the pot when he's holding AK-AJ for no reason. And I think just getting called by some lower flushdraws which we also block with the Tc is not enough reason to bet for me. Also having the nut flush draw makes it a bit more attractive to bet. Without the fd this turn would be a clear check for me.

3) I guess the river might depend strongly on whether we expect him to donk-lead with AK here and even AQ. As he has all offsuit and suited combos of these this would explode his value range. I guess that especially at the micros we could expect to see some donks with AQ here? He might lead with some of his sets but chances are good he would check-raise them either on flop or turn. JT he could lead just as well. But with the missed flush draw on the board he should also elect to trap your bluffs on this river check-raising sets and JT and calling AK/AQ probably. So this should move some of his value hands to his checking range...Which makes a call better. We block JT...but we also have AK-AJ to call in our range. Probably AJ is no difference to AT but AQ, AK are way better calls.
I guess blocking flushdraws and the straight and 'only' having AT I find a fold here.

As you see I'm unsure about almost every decision here myself. I'm really looking forward to get some thoughts of more people.

I think I would find a fold here. The analysis above is very solid. I am actually really curious what UTG has there. First, the sizing he uses 2/3 pot does not look like a block bet to me, so I don't think he has some weird pair of 9s, or 10s and Js. Therefore, it's polarized to value and bluffs. When you block the 10c, there is probably just 67c (if he decides his 7 sdv not good, which I would say that's unlikely what he's doing) , QJc, KQc. Therefore, I don't think I can find enough bluffs here. The reason that you should not call is A10 is probably the bottom of your value range. When you take the line bet bet, you could potentially squeezed utg with 10Js (although not advised by snowie) or 56s (which is advised by snowie) which got there, or 89s which flop topped two, or even a nut flush draw with better kicker, or even betting the flop with only Ac as backdoor flush draw with better kicker (AK,AQ (altough AQo is advised to fold to utg open)). Therefore, you have a lot more hands in this spot that you are gonna call with. The only other hands that are worse than A10s, is probably A2s,A3s,A5s,A6s, so given the sizing and you even blocked some flush draw combos, I think A10s should be a fold.

I think you want fd's in both your x and bet range on the flop. In srp I balance by checking nutfds behind, bc they are more likely to win at sd in improved. Think checking flop is viable option. As played I'd bet turn, bc this card is great for our range and I'd bet a great deal of my air, if not al.

One of the biggest leaks a lot of microplayers have is Un unbalanced check range. It's also very easy to exploit; just bet as they check. What kind of hands do you x flop that can call a turn bet, especially on this board type? If you bet all your value hands and draws, it's probably skewed towards air.

I actually like the hand as played.

I think the board is ok to c-bet flop 1/3 pot size with 100% frequency, then you also don't have to worry about balancing your check back range.

Turn is a good card for you and you should barrel a lot on this card. It's especially good for your particular hand where you get thin value from worse and build up the pot for river in case you hit your flush. I also like your sizing.

On the river, his donk makes almost no sense. He's representing JTs, 87s and possibly 97s. As far as his AQ, AK hands go, he should be bluff catching river with those hands especially after flush draw busts. And even if he does donk river with AQ/AK that's worth calling to see and making a note because then his river checking range will be way too weak. But in general his donk looks like a desperate attempt at winning the pot due to your small bets and I would make the call.

The downside of bluff catching AcTc is we block lots of his potential bluffs with Tc, but I still believe he will lack value hands here.

At 10 nl I used to bet half to 65% on flops like this to clean up some high card outs and bluff outs. Also gotta think if you have JJ Or QQ and you wanna get a little more money in early before a bad card hits for your hand or a scare card which kills your value. In position I would either check back the turn trying to pot control and induce a bluff or get a lighter call down from pp thinking you would've bet your ace to get value from fd.

Your turn small sizing definitely induced him to spew and I would say if you had bet larger on the turn and he donked it would be a clear fold as he would always have jts. These river donks at micros are literally almost always always rivered flushes and straights. In some fashion I like your call more than an AJ or AQ call because of the T Blockeure