Puzzle 1: Red to move and win
Solution

Black's rook is already imprisoned, Red's task is quite simple, he has to close all doors and windows of the prison before he can collect the rook.

1. E5+3      
2 points, prevents that the rook can escape with 1. ... R9-2
1. ... A5+4
Red can follow his plane irrespective of the concrete moves of Black's defenders. Therefore, here and for the following moves I give only one example for Black's reply. Only in the case of a rook move Red may have to change his move order. Whenever Black takes the pawn with R9-3, Red will capture this rook with H3+1 reaching the won endgame cannon and horse vs. two elephants and two advisors. (e.g. Answer3)
2. E7+5
1 point
2. ... A4+5
3. K4+1
1 point
3. ... A5-6
  3. ... R9.5
4. E5-3 K5.4
5. E3-1 K4.5
6. C3.5 K5.4
7. C5-3
1 point (Answer2)
4. E5-3 A6+5
5. E3-1
1 point, now the prison is secured, the cannon is free and can easily capture the rook.
5. ... A5+6
6. P1+1 A6-5
7. C3.1 K5.4
8. C1-3
1 point for the last moves of the main line (Answer1)
Puzzle 2: Red to move and checkmate
Solution

Red's attack on the 6th file is very strong, Red can easily force a checkmate.

1. C7+7      
2 points, the threat is 2.R++5 mate (Answer6)
1. ... E5-3
  1. ... A5+6
2. R++5 K5+1
3. R-+7 mate
1 point (Answer4)
1. ... E1-3
2. K5.6 A5+6
3. R++5 K5+1
4. R-+7 mate
1 point (Answer5)
1. ... A5+4
2. R++3 and Red has still the threat 3.R++5 mate, 1 point
Moves like 1. ... R2.4 2.R++1 or 1. ... C5.4 2.R++2 can't resolve Red's threats.
2. K5.6
1 point, threatening 3.R++5 A5-4 4.R6+8 mate (Answer3)
2. ... A5+6
  2. ... A5+4
3. R++3 A6+5
4. R++2 A5-4
5. R6+8 mate
1 point (Answer2)
3. R++5 K5+1
4. R-+7 K5+1
5. R-1 K5-1
6. R+-1 K5-1
7. R-.5 A6+5
8. R6+1 mate
1 point for the last moves of the main line (Answer1)
Puzzle 3: Red to move and checkmate
Solution

Red seems to be in trouble, Black is not only threatening checkmate (beginning with R7+1), the black horse is also attacking Red's rook and horse. Nevertheless, Red can force a running mate.

1. C5.9      
2 points, as we will see later this cannon is on it's way to Black's base line!
1. ... H7+5
  1. ... A6+5
2. P6+1 K5.4
3. R7+9
1 point
3. ... E1-3
4. C9+5 E3+5 Or E3+1
5. H8+7 K4+1
6. R5.6 A5+4
7. R6+5
1 point (Answer3)
1. ... A4+5
2. R7+9 E1-3
3. C9+5 E3+1
4. H8+7 mate
1 point
1. ... H7-5 2. R5+2 doesn't help
2. P6+1
1 point
2. ... K5.4
  2. ... K5+1
3. R7+8 K5+1
4. H2+4 K5.6
    4. ... K5.4
5. R7.6 mate
  5. H8+6 K6-1
6. H6-5
1 point
6. ... K6+1
    6. ... K6-1
7. R7.4 mate
  7. R7.4 mate
7. R7.4 K6.5
8. C9.5 K5.4
9. R4.6 mate
1 point (Answer2)
3. R7+9
1 point
3. ... E1-3
4. C9+5 E3+5
  Or E3+1
5. H8+7 K4+1
6. H2+4 mate
1 point for the last moves of the main line (Answer1)