I would check the flop sometimes and bet sometimes. Pretty good hand to check from time to time in my opinion so that we can have hands to calldown when an A comes, there are tons of turns that we can continue on, and we induce him to bet with air and we can showdown, and also turn our hand into a bluff on some runouts. There are a lot of options with this hand on many turns and rivers by both calling and betting the flop.

On the turn I would either bet or check/fold, I'm not sure how I feel about check/calling or check/raising. Betting is indeed a pretty cool option because we should have some FE and we can triple bunch of rivers, mainly spade ones. I would probably size my turn bet bigger and put more presure to his 98/7x/weak flushdraw hands. I would probably bet potsize bet or consider overbetting.

On the river we do have a decent bluffing hand. We don't have that many air hands anymore when the 9 comes. A hand with a heart and without a spade would be better obviously, but I think this is a decent hand to bet the river. I like your sizing but again, we could consider overbetting. Overbetting might be a better option with a heart though, since we really should block the nuts or very strong hands (in this case flushes) if we want to overbet.

You block some of his top pair combos; turn play is really just bet again or x/fold, you cannot x/call with a high and a gutshot when villain most likely has SDV or a flushdraw which will outplay you on most rivers. X/raising turn polarizes your range too far and is only adviced with some specific read.