all players are unk

Opening 3x 97s from MP1, I plan on folding vs any aggression(gonna flat to min 3bet though and play fit or fold on flop). I assume BTN calling range to be mostly pp, weaker brodways, suited connectors.

BTW what do you think the optimal raise sizing is preante?

I hit fd and lower gutshot and I think my opening range hits this flop more often than my opponent, so I think a cbet is a must in this spot. I'm not sure however if this sizing is optimal. Now I think I should bet a bit smaller(around 55) as we are getting almost the same fold equity - I believe he's not going to fold any pair, fd, oesd, Ax to any sizing and he's going to fold lower pp and weakish suited connectors. Is my thought process correct?

I believe an ace to be a great barreling as it improves my range significantly. I believe I have two options here - first one is to check/give up, and second one which I enjoy much - bet turn with the intention of double barrel on river to fold as his Kx, Qx, Tx, 2pairs combos which he should be folding to tripple barrel. Again I think this sizing is too big and I should bet around 125. Even if the villain calls I still may hit my flush and get value from villain's hands.

On this river I decided to bet small(again what do you think about this sizing) with the intention of folding all his missed draws, Kx, Qx, Tx, some Ax, and sometimes his 2p. I'm planing on folding vs any aggresion here. Should I bet here or just x/f?