I try to put the villain on a range from the start and then trust myself (and yes sometimes I miss the range).
If he is complete unknown (lets say it is his 1st hand since he is in BB) I usually assume by default he calls with pocket pairs or Axs/suited Broadways, these being often shown from blinds.
If he just calls 2 barrels, I tentatively evaluate him as a loose passive (many TAGs raise their flush draws and generally don't call 2 barrels from an unknown OOP). If he is a nit then he has a set and you are dead.
1) Since you are in position and he checked to you, I check back so I don't get blown off my hand and I want to see what did he call with.
- No way he folds a flush and if he called with a set likewise so why am I betting? Take the showdown, make a note on him, life goes on.
2) Fold. I am not happy about it but such is life. Put a note on it and observe his play, if he likes bluffing
long term you will get him back. I have one of these on my tables, he is hilarious I play my draws aggressively so when flush comes he is guaranteed to shove into me for easy money. Seems he is getting paranoid these days though
3) This one is difficult... I think check call (depending on his bet size) is best, often I can catch random crap that took a shot at the pot. If he shoves for a lot of $$$ I usually fold without any reads.
4) This is actually good. If he always fires, we catch quite a few bluffs at least in 5NL, not to mention that we get his stack every time when we have the flush