TT set

I always C bet here (in position). You want to fill the pot. I think checking here is a mistake.

I would not fold river. two pair hands, lower sets, 88,99 are also in his range and what is the chance he is siting with 35 (suited)?
So only hand that beats you is 89 i think.

I don't think that 88 and 99 bets a pot OTR.
He might also have 55, 65s.

You can check but you could also go straight for value and start betting OTF. I think that might be slightly better at NL5.
OTR I would say that "theoretically" this is absolutely a call. If you want to fold this hand, the decision would be based on that you believe villain will almost never donk the river without the nuts.

I think 55 is the only 5x hand that should be in SB's calling range pre-flop. But this is NL5 and we don't have much info on villain. Overfolding might be a decent idea here. Personally I wouldn't be able to give up top set, so this is totally up to you

How can you suggest that checking is good here. BET!

The flop is dry as a bone. It is difficult to balance our betting range here. We do not need protection and by checking the flop we might get better action. But I do agree that betting might be slightly better at NL5. That is why I said we can check but going straight for value could be slightly better at NL5.

I don't see occasional checking here as a mistake.

This is a mistake as pairs will call, overcards will call. Backdoors may call too. Why miss all that money?

I already said twice that I prefer betting small OTF more in this situation. That "we can check" part was just a more balanced point of view.
But anyway, if we focus on exploitative play only, maybe checking still wouldn't be a terrible idea. Yes there could be some pocket pairs that could call, but they are not likely to call all 3 streets anyway. If we check the flop and give one more card (not dangerous for us on this board), don't you think we might get more action OTT and OTR.

You are right that betting is ok. I just wouldn't call checking as a mistake. Of course depends a bit on your point of view.