endgame

IIRC your second problem was either composed or played by Capablanca.

Your solution to the third problem is about three moves too long. Any path which brings the knight to c8 in three moves followed by Bd5 is mate. Examples: Nb7, Nd6, Nc8, Bd5  or Na4, Nb6, Nc8, Bd5, or Ne4,Nd6,Nc8, Bd5 etc.

ok thank you

is this better?

i was unaware of that, about the fourth one i just posted not long ago, i know it was a game, just not sure which one

Your fourth puzzle was from a game won by Alekhine. The victim was Capablanca.

These are good puzzles.

Does the first puzzle succeed in having a unique solution?

Yes, but I don't think it has a unique solution. 1. Kf1 is not the only way to draw. 1. Kf3 also achieves the goal, if I'm not mistaken.