These scenarios all pertain to being 100bb's or so deep.

Scenario 1: If we are in position as the PFR in a 2bet pot, and we flop a gutshot, should we typically bet this or check it back?

Betting it is good if our opponent calls as we can check back the turn and try to hit our 4 outer twice.

However if our opponent check/raises we typically have to fold with 100bb stacks as we are typically looking to call about 8bb or more and even if we hit on the turn we may only have 80% equity or so vs our opponent's range that stacks off with us, slightly reducing our implied odds even further.

If instead we check back the flop, then we can realise our equity for free, and if the turn doesn't pair the board, we can usually call a turn lead from our opponent and so get to the river for only 3bb or 4bb extra and fully realise our equity.

Scenario 2: If we are in position as the PFR in a 2bet pot, and we flop a flush draw on a paired flop, should we typically bet this or check it back?

Again betting is good if our opponent just calls our cbet, as we can just check back the turn and get there a fair amount of the time.

However if our opponent raises, this could be with an under full which we are already drawing dead against, or trips where a lot of our flush outs can be dirty and so again calling a check/raise seems unpalatable so we usually just have to fold our flush draw on the flop to avoid reverse implied odds right? This seems like a waste of equity.

Scenario 3: If we are out of position as the PFR in a 3bet pot, and we flop a flush draw on a paired flop, should we typically bet this or try to realise our equity for cheap by check/calling and hoping a street checks through?

Again our opponent may have flopped a boat or trips so happily semi-bluffing away seems scary when you could already be dead or almost dead. Is it better to try and play for a small or medium pot if we can?

I understand that these are general rules of thumb that I am asking about here, but it is good to understand different people's thought processes about these common types of situation and how they try to realise their equity whilst also minimising losing big pots unnecessarily.

I think you should also take in consideration the flop texture and the range advantage.

On certain flops we will Cbet range, with a small sizing.

On other ones we will bet polarized. And on these ones, we usually want to bet our strong value hands and our best draws. Sometime we have many draws so we dont need to bet our gutshots. Sometime we have so few and they become an easy bet.

If on some boards we have few gutshots, doesn't this mean that our opponent can check/raise us more as we have less made hands and draws on that flop, thereby just wasting the few gutshots we do have, needlessly in that scenario?