Puzzle 1: Red to move and win
Solution

Black has the mate threat 1. ... R++3 2.K6-1 R++1 3.K6+1 R-+6. The defence 1. R6+3 is not sufficient because of 1. ... R++3 2.K6-1 R++1 3.K6+1 R-+6 4.K6+1 R+.4 checkmate. The other passive defence 1.R7+4 K4+1 2.R7-1 K4-1 3.R6.2 doesn't help, since Black has 3. ... R+.4 4.R2.6 R4+2 5.K6+1 K4.5. Therefore Red has to choose a more agressive approach:
1. R7+4 K4+1
2. R7-1 K4-1
3. R7.5
      
3 points, this multi purpose move parries Black's mate threat, immobilizes Black's king and prepares the advance of Red's pawn. Capturing Red's rook or pawn turns out to be insufficient, instead Black can't do much but watching how Red's pawn gets closer and closer.
3. ... R--1
  3. ... R+-1
Or other waiting moves of Black's rook
4. P1+1 R++1
If Black captures Red's pawn here or later, Red will win as shown after 9. ... R-.6 in this line
5. P1+1 R+-1
6. P1+1 R+-1
7. P1.2 R++2
8. P2.3 R+-1
9. P3.4 R-.6
10. R5-3 R6.7
11. R5.6 K4.5
12.R++2
2 points, Red wins

3. ... R++3
4. K6-1 R++1
5. K6+1 R-+6
6. R5-7 R5-1
7. K6.5 K4+1
8. R6+1 K4-1
9. R6+4 mate
1 point
4. R6+5 R-.4
  4. ... K4.5
5. R6+2 mate (Answer2)
5. R6+1 K4.5
6. P1+1
1 point for the last moves of the main line (Answer1), the end game rook and pawn vs. rook is an easy win for Red as long as the pawn does not become a veteran. This is an exemplary line: 6. ... R5-2 7.R6-3 R5+5 8.K6-1 R5-5 9.P1.2 R5+6 10.K6+1 R5-6 11.P2.3 R5+5 12.K6-1 R5-5 13.P3.4 K5.6 14.R6.5 R5.4 15.K6.5 R4+2 16.P4.3 R4.6 17.R5.4
Puzzle 2: Red to move and checkmate
Solution

With two rooks and one horse against cannon and two pawns Black seems to have an overwhelming material advantage. But both rooks are awkwardly placed and Black's high king is without any real protection. The first moves are quite obvious for Red, for the final checkmate he needs a little trick.
1. C2.5 H7+5      
  1. ... K5.6
2. P-+1 K6-1
3. P4+1 mate
1 point (Answer5)
2. P-.5
Threatening 3. P5+1 mate
2. ... A4-5
  2. ... R4+1
3. P5+1 mate
Answer4
3. P5+1
1 point
3. ... K5.4
4. P5.6 K4-1
5. C5.6
1 point
5. ... A5+4
6. P4.5
2 points
6. ... K4.5
  6. ... R5+1
7. P6.5 mate
Answer3
7. P6.5
1 point
7. ... E3+1
  7. ... R4+1
8. P5+1 K5+1
9. C6.5 mate
1 point (Answer2)
8. P5+1 K5+1
9. C6.5 mate
1 point for the last moves of the main line (Answer1)
Puzzle 3: Red to move and checkmate
Solution

If Red's attack doesn't succeed he will be without sufficient attack against Black's threats. However, Red moves first and has a running mate at hand.
1. R4+7      
2 points
1. ... K5.6
2. P3+1 K6+1
  2. ... K6.5
3. P3.4 mate
Answer 7
3. H3-4
1 point
3. ... R8.6
4. H4+5
1 point
4. ... R6.7
  4. ... R6+1
5. H5-3 K6+1
6. H3-5 K6-1
7. H5+6 K6+1
8. H6-5 K6-1
9. R6.5 mate
1 point (Answer4)
5. C5.4 R7.6
  5. ... P5.6
6. H5-4 mate
Answer3
6. H5-3 K6+1
7. H3-5
1 point
7. ... K6-1
  7. ... K6.5
8. C+.5 mate
Answer5
8. H5+6
1 point
8. ... E3-5
  8. ... K6+1
9. H6-5 K6-1
10. C+.5 R6+1
11. R6.5 mate
1 point(Answer2)
9. C+.5 R6+1
10. R6.5 K6+1
11. H6-5 mate
2 points for the last moves of the main line (Answer1)