1. You call the first one easy? it is a not so easy endgame puzzle, and one which I haven't seen before. Smart move with the king, keeping all options open for the bishops.
2. In the second puzzle, I assumed that white needs to take the knight and follow up with precise moves in a winning pawn endgame. It is an elusively deep tempo analysis though. One ought to calculate far ahead in advance.
3. The third puzzle, finally, was kind of obvious, despite being long. There aren't many options to consider... Rxb1+ is the first move to calculate, and the moves are forced with a good string of checks. The description is slightly misleading though, as "find a way to save the game" sounds as if one is fighting for a draw.
4. The fourth one, of course, was kind of ridicilous. The thing about it, however, is that an experienced solver might find the right moves due to them being ridicilous, and the most surprising moves in the position. 1. Bb1!!, with the idea of almost leaving black with no good moves, and 4. g8=B! are the kind of moves composers love, and good solvers look for (when it seems to be 'that' kind of puzzle 
).
5. Just a bit too hard on the exclamation marks.
Thanks a lot for sharing these wonderful puzzles!
The only way I could solve that one in a minute or two is to punch it into Nalimov (which I did...and it gives a mate in 27).
Instead of opening new topics all the time i decided to post some interesting puzzles here.
•1)Let's start with a rather easy one that every good Chess player that respects himself should solve within 1 minute or 2.
•2)Then let's see how white can win this game. There is only one move that wins in all the first 3 moves so it's really difficult. One mistake and it's over for white.
•3)And now one that black is a Bishop and a Knight behind in material, so he has to find a way to save the game.
How?
•4)And now a tough one. White is a Knight and a Pawn up but black threatens to promote to a Queen with 2 connected passed Pawns on the 2th rank. White can indeed save the game and win. But only playing some amazing and very accurate moves! How?