No.

For me this flop is a range-check 3way 2nd to act.
As played you should fold flop. Reason is that your hand is very hard to improve, and you are facing a lot of action (btn raise, bb coldcall a raise) so therefore I would just let it go on the flop and not be in a poopy spot whenever I hit an A on the turn and face a big bet forcing me to catch unlikely bluffs.
Once you get to the river there is obviously no getting away from that hand. Not sure I like the lead or the sizing that you chose.

Imo you shouldn't really have ended up on this river in the first place as flop is a clear fold facing this action. Also as said above, I would be looking to check this flop very often and your sizing when betting is way too large. You say you have better odds when BB cold calls the raise but that just means that there is one more player with a strong range and you have very little outs to improve. River I'd either check or block bet as you still get raised by boats and he might fold a flush Vs this sizing. As played there's no way getting away from it, you have top boat

When you bet the flop you should have a plan for later streets and also consider your range. You don't have many hands that want to bet 3 streets for value so checking full range in this spot makes sense and makes your range easier to play on future streets. Also with your sizing, you don't get more fold equity with your bluffs and you fold out hands that you crush so it doesn't make sense. If you're betting (which I probably wouldn't suggest anyway) a smaller sizing works better for your range

Definitely don't range check at 5nl with TPTK (BB is understacked too so makes it even worse)

Flop sucks, I can totally see how you ended up otr here given pot odds, but this is a great example of reverse implied odds that compounds when you make smaller mistake earlier in the hand.

Flop is a fold, since they are raising 3w repping like, flushes and sets and the BB calls as well (doesn't mean they're nutted but often strong and it reduces our equity further making our pot odds less attractive).

So yea, fold earlier but turn and river are wp. Your reasoning makes sense and unlucky if you lost. Didn't have a royal did he? lol

Gotta pitch it on flop, especially when you bet over 75% pot on mono board and got raised in a 3 way pot, not to mention the BB cold call. Reverse implied odds are astronomical here.

Flop bet should be smaller also.

That is one of the two good turns you could hit. So, from the flop on, it seems well played.