Villain is an unknown.

My questions are:
1) Are we always just check giving up in such a situation when the turn pairs unless we have the pairing care for trips? (Specially against unknowns).

2) Would my line be okay versus people who float flops often say like a fold to flop cbet below 50%? In what cases would the line I took be good?

3) Are we definitely betting the river when we bet this turn and don't get raised to get villain of his draws? (when we do decide that the bluff line is appropriate)

My thinking is that first off this was clearly bad play on my part since the standard line would be to check/fold this turn versus an unknown villain or a more straight forward villain who folds to cbets more and has a tighter range on the turn. Just don't think this was a good experiment on my part but my question is about a more general sense when would it be exceptable for me to take this alternate line. In this case the fact that I have 2 flush cards actually makes my bluff worse.

Barreling turn here is fine. You force a lot of weak draws i.e. hands that have good equity against you to give up.

Any decent player shouldn't be folding to flop cbets with top pair+ side cards in heads up pots like this given it has equity against say AAxx and is often the best hand, so it's reasonable to assume that villain's get to this turn with a lot of top pair type hands as well as all the draws and medium strength stuff that will probably fold to a turn barrel.

After getting called on the turn I probably x/give up on the river. Hard to see 0.02/0.05c players having a wide range by this river. I expect them to have Kx or better a tonne since (I assume) they have really nitty continuation ranges.

As for your question, barreling these turns is especially good against low fold to cbet players because of how often they're floating with air or weak draws and hands, although some smart aggressive players will know this and can potentially raise your turn barrels on these cards with their floats but I honestly wouldn't ever worry about that at PLO5.

tl;dr turn barrel is fine, give up river as played.

You are right in most of your assumptions other than about the nitty continuation range on the paired turn. This is player dependent. I have seen loose passive players and maniacs continue calling on the turn with their flush and straight draws on paired turns. On the other hand Nits/Tags/Lags tend to fold or have it after the turn as you said.

In this case the villain over a tiny sample 20 hands was 90/55 and a loose passive calling station post. So I assumed he is capable of having the missed straight and flushes on the river besides the K.

I normally do take the line you mentioned.

You need to bet a little bigger for a bluff to work. Otherwise vs unknowns you're getting a lot of routine unthinking chases.

Unknowns just tend to be stations, and a huge part of villain's range (any king) is autocalling. A bet with air would be horrendous here and I think a semibluff with what you have is going to be marginal at best. Nothing wrong with leaning toward aggression in marginal spots though.

this, although you should size up a bit on the turn, or you will get very few folds

I don't see a reason to bet flop. We aren't betting for value/protection against anything and we aren't folding out much better at all (especially vs fish)

Barreling paired turns is usually a good play since all draws are now longer to the nuts given their is a possible FH out there. Although it's usually better if it's not the highest card paired (since they will have more Kx than Tx) - in addition, Kx now also loses to AA.

However, vs this villain I probably just give up.

Okay. Thanks for all the responses

In general I don't mind this approach. Obviously if it is draw vs draw, esp. with your weak draw, and you can win on the turn with a bet then that is nice. I feel like checking the flop is the superior choice as you are out of position with a truly marginal holding.