Is it worth exchange knight to pawn?

Not unless you calculate it and truly believe the result is a clear advantage.

I might go for it against a weaker player if I though it would end up two pawns for the knight. (It is good to experiment sometimes - but not in a game that was important, like it made a difference between 2nd and 3rd place in a tournament).

-But unless you clearly calculated:

a) A mating net, or

b) Forced return of material (i.e. they have to give a piece back to avoid mate).

I wouldn't.

I certainly wouldn't expect to get away with it without clear compensation unless it was a much weaker player, and bullying weaker players this way is

a) Not a good sporting way to play chess.

b) Not a good way to learn.

c) A formula for getting sucker punched by the revenge of the weaker player you've underestimated.

And just for the record, these combinations usually begin with the bishop check, as this gives initiative.

There are games where a player will sacrifice his knight for a pawn to exposed the enemy king. Now if you are not good at tactics and calculation, 95% percent you will lose the game. To make such sacrifice, you must be good at tactics and calculation. If you are a novice level, solve tactics problems everyday.

If you want to study how to attack at chess, The Art of Attack is a good book to get. But as I told, improve your calculation and tactics. Solve tactics problems appropriate for your level.

I would strongly advice against it for beginners and even early intermediates. Unless you clearly see a checkmate in two or three of your moves then it isn't worth it to just expose his king with no follow up moves in mind. Often advanced players will do this against beginners because they know they're so good that they'll get the material back. Two evenly matched opponents is a different can of worms.

Impossible to answer this without seeing the specific position.

However, there are many examples of a crushing attack following e.g White's Nxf7 or Nxh7, forcing the king to retake and thus expose himself to attack. The sacrifice would need precise calculation, and a well developed deployment of pieces to follow it up.

Not unless you can checkmate in 2-3 moves.

like most things in chess, it depends on the board. but i don't sacrifice anything unless i see a follow up combination to attack.

Yeah.

Very extreme.