BN needs 32% equity to call your shove. So they would probably call most flush draws/straight draw/combo draws. Your check-raise shove looks a bit bluffy, so they might call you with some top pairs as well. Thus your line seems fine to me.

I would have just bet the flop because you're multiway and someone should have flopped something. You can get value from a flopped middle pair and weaker hands.

I prefer a bet as well, you will get more value from worse hands.
Now when you push you are pretty much in the dark if we are behind or in front.

looking at ranges I think your push is still ok. He is going to have a bunch of FD, some Jx and some straight draws with a pair...

sqz size is small. As played doesn't matter much(bet/ or x/R) as long as you don't have information (stabbing too much)