Looks fine with no draw or equity, I would sometimes bet here once to fold their hands with no equity that may bluff us, but think c-f here is toally fine.

x/f here seems decent. If you want to be bluffing any no pair no draw hands here then I think Ax and Kx hands will be best since they'll likely have the most equity when called but on this texture that doesn't seem very attractive. I'd probably bet a Q73ccc since there's less broadway connectivity than Q93.

I don't think your play is weak given the unfavorable board texture. It's not like you have the same amount of showdown value than you would on something like Qs7h2h etc. Folding the flop is totally fine.

It's often easier to ask yourself how many turn cards are you happy to see compared to bad turn cards. Here you have absolutely nothing to look forward to, and there's a lot of combos BTN could have which are never folding.