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The only mistake I really think I made here was not checking behind on the turn. I really didn't have much to lose by doing that. I'm torn on calling/raising the flop. Equity-wise, raising is fine, but only if you don't make a big mistake like I did on the turn ("mistake" from a Fund. Theory of Poker perspective). So waiting on a safe turn is probably the better play since a mistake will generally cost you less.

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Yeah, the bigger mistake was definitely betting the turn. However, I'm not sure that raising the flop is correct "equity-wise". (Can you explain what you mean?) Twodimes won't work here because you're not all-in. You'd have to count the number of turn cards that you'll feel safe betting, multiply that by your win% with those cards, and then count all the other turn cards as zeros, assuming you'll have to fold to any action they bring. Raising prob isn't equity-wise correct IMO