If it's a critical error like hanging a piece with no compensation, explain why the move is a mistake ask why they made the move, and then explain why their line of thinking was wrong, etc.
Of course this is if it's a teaching game, if you're playing a game but you want to help the player, analyze the game post-mortem, yes.
It depends entirely on what you are doing. If you are playing a game, play it out and analyse it later. If you are giving a lesson, give a lesson.
For me its fairly simple, if anything can be learned from playing it out then play it out. If its a blunder & playing it out will just be a waste of time then give them the move back.
Definitely an take-back. Especially if it's an outright blunder. Really think it's an waste of time to discuss post-mortem if it's just an training game. The exception is after him (or her) winning or losing to someone other than myself (post-mortem analyses, not take-backs)
If you crush them mercilessly it will have a more profound effect - good or bad.
BDJ is right on that one
If you are playing a game, you should play according to the rules, including touch-move.
If you are teaching someone, the benefit of playing a game against them may not be as great as a lesson. But whenever you do play a game, you should follow the rules. That is an important principle.
Let say you want someone to improve, and you are helping him/her. When you play a game should you give a take back when he/she comitted a mistake? Or analyze the game later when the game is finished?