1) I'm leading out on the turn for 3/4 the pot and calling a push. Your check makes your hand look very weak so villian will bet with just about anything here. As played I probably check-raise all-in on the turn, you've got mad fold equity here and have a ton of outs you can hit.

2) Obvious fold on the river, you can only really beat a bluff and the way this went down it's almost never a bluff here. Leading out on the turn is okay but to keep the pot small I might just check/call in that situation.

3) Push and pray you hit one of your outs or everyone else folds. Other people would probably disagree with that.