If somebody playing with you propose a takeback, how often will you accept it? Do you know if takebacks are allowed on tournaments?
Regarding tournaments, according to the FIDE rules, takebacks are not permitted. Section 4.6:
When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is then considered to have been made:
(The rest of section four has more rules about touching a piece, moving a piece, capturing a piece, and the like - but the gist of the answer is there: once a move is made, it has been made.)
Regarding casual games... that's entirely up to you. In general, I prefer touch move and no takebacks regardless of the game - but sometimes, if it was a very good game, it's nice to say, "sure, you win... but what would have happened if..." and play it out a different way.
I'll generally accept takebacks when playing online if I suspect the move isn't what my opponent actually intended, and have actually been known to request them under the same circumstances (I can't tell you how many times I've tried to castle on the Lichess mobile app, and ended up just making a king move instead by accident, just because of how the user interface works).
I never propose takebacks in over-the-board play, and generally wouldn't agree to an opponent's takeback proposal unless it's a very casual "just playing to while away some time" type of game - when playing over-the-board, it's unlikely to make a move that isn't what you actually intended. While I haven't really thought about it to any extent, I think my boundary line for this would probably be, if the game is serious enough that a clock is involved, then it's serious enough for both players to be held to all the rules...
Only on local tournaments in friendly atmosphere, with very weak opposition in first rounds, where my risk is minimal and nobody cares. Even if I liked showing respect to some world class player, unexpectedly blundering, maybe offering conditional take back, where he can no longer win the game, you must understand that you are breaking rules and you can hurt other participant seriously with that. That's place where you don't want to be. I won every game easily where I allowed takeback.