I am going back and forth on how to play this flop.
Assuming no fish at the table I would open about: 55+,A8s+,A5s-A2s,KTs+,QTs+,JTs,T9s,98s,87s,AJo+,KQo, and so our equity vs QQ-55,AQs-A9s,A5s,KJs+,QJs,JTs,AQo+ is only 48,75% on that flop (Of course it gets better if villain 3bets QQ, which he might) Should we just check most of our hands or still cbet like AQ+ and most of our draws and some backdoors and then x/c Qx, JJ/TT, 9x and some draws?

I would assume villain to continue vs a bet with 9x+, JTs, KJs, KTs, and all FD's and maybe AxKd. Do you think He will raise sets and some draws, or call everything?

Assuming we have cbet flop with most of our FDs and strong madehands, do we keep barreling most of that range and bluff with AdJ and AdK and maybe JTs?
Or do we check a wider range to let him fire his gutters, maybe AxKd, and bet only flushes and some draws, and x/c some flushes, sets and AQ-AA?
Or even check everything? Lots of strategic options on the turn imo.

Not sure how many hands villain folds on the turn, likely JJ/TT without a diamond, KJs, KTs, probably also JTs. What about QJ with no diamond or TT with a diamond?

Finally concentrating on our actual hand on the river, do we bluff here?
Depending on how wide villain calls turn, and given that he cant have many draws given that we have the Ad and he wont have KJo/KTo/JTo with 1 diamond we likely need him to fold most Qx in order for our bluff to be profitable.
I am not sure if villain would think that we may check flop or turn with some of the hands that are boats by the river? OR if he may assumes that we check some flushes on the river?