Villain 42 hands - 32/17 - basically unknown

On the flop I guess this hand can be either played as small bet - 33%or somthing like this as this flop is better for our range or check/call.

I chose check/call as it seems bit easier to play in these spots.

What shall we do on the turn tho vs this bet and sizing ? X/C again and re-evaluate on the river? I have better TX hands in my range and I will even sometimes slowplay monster hands in this spot so I have my X/C range protected. T9s and 99 is bottom of my range basically so we can fold I guess..

How shall we construct our range on this flop? My open range: 55+, ATs+, A5s-A2s, KTs+, QTs+, JTs, T9s, 98s, 87s, AJo+, KQo - 176 combos

Cbet - TT, QQ+, AKo, AQ, AJ, KQ, KJs, QTs - ca 84 combos - shall we cbet all with AJo and AKo or not? Will we bluff too much if bet all of them ? It will be like 33% of bluffs then but we still have equity with these hands especially with AKs and AJs with backdoors.
X/F with A5s-A2s or cbet combos with backdoors? Cbet seems too wide. 87s , 55-88 - 44 combos
X/C JJ, 99-88, ATs, KTs, QJs, JTs, T9s, sometimes AJs with backdoor so I can have some flushes and SD on later streets, sometimes QQ so my range isn't capped once I Check the flop, sometimes 98s, (98s cause I want to have some hands without showdown value I can bluff with on turn or river after checking flop so I will stay balanced when I bet or reraise with my strong hands -QQ for ex.) - total of 43 combos

Therefore we will cbet smth like 50% and X/F 25%, X/C 25% - roughly....it's not optimal to fold 50% of times we check the flop but we are OOP so it's hard to defend 100% unexploitably.

Anyone with solver please? :D I'm interested what sizing and range would solver cbet and X/C and X/F here.