Puzzle 1: Red to move and win
Solution

Black has two horses and two advisors against three pawns, but king and one horse are in a cramped position and Red's pawns are very dangerous. However, the simple 1. P+.6 K4+1 2.P7+1 K4-1 3.P4+1 H3-5 is not enough for Red. He needs a more tricky plan:
1. K6.5      
1 point threatening 2. P7+1 checkmate
1. ... A4-5
  1. ... H4+6
2. P++1 K4+1
3. P-+1 (Answer 16)

1. ... A6+5
2. P4+1 H3-2
3. P-.8 A5-6
4. P7+1
1 point (Answer 17)

1. ... H3-5
2. P-.6 K4.5
3. P6+1 A6+5
4. P6.5 K5.4
5. P7.6 H5-4
6. P5+1
1 point (Answer 18)
2. P-.6
1 point
2. ... H3-5
  2. ... H3-4
3. P4+1 A5-6
4. P7+1 (Answer 14)

2. ... A5+4 3. P7+1 (Answer 15)
3. P6.5 K4.5
  3. ... A5+6
4. K5.6 H5+4
    4. ... H5-3
5. P4+1 H3-1
6. P7.6 (Answer 10)
  5. P5.6 A6-5
6. P7.6 K4.5
7. P-.5 A5-4
    7. ... H4-3
8. P5+1 A6+5
9. P6.5 (Answer 7)

7. ... A5+4
8. P5.6 H4-3
9. P++1 K5.4
10. P6+1 H3-4
11. P4+1
1 point (Answer 8)

7. ... A5+6
8. P5.4 H4+5
9. K6+1 H5-4
10. P-.5 H4-5
11. P5+1 A6+5
12. P6.5
1 point (Answer 9)
  8. P6+1 K5.4
9. P4+1 K4+1
10. P4.5
1 point (Answer 6)

3. ... H5-7
4. K5.6 A5+4
5. P7.6 K4.5
    5. ... K4+1
6. P5.6 K4-1
7. P6+1 K4.5
8. P6+1 (Answer 13)
  6. P5.6 H7+5
    6. ... A6+5
7. P+.5 H7-5
8. P6+1 H5+4
9. K6+1 H4+3
10. P6+1 (Answer 12)
  7. P++1 K5.4
8. P6+1 H5-4
9. P4+1
1 point (Answer 10)
4. P5+1 A6+5
  4. ... K5.4
5. P7+1 (Answer 5)
5. P7.6 H5-4
  5. ... A5+4
6. K5+1 A4-5
7. P6.5 K5.4
8. P4+1 H5-3
9. P4.5
0.5 points (Answer 3)

5. ... H5-7
6. P4.5 K5.6
7. K5+1 H7+5
8. P6+1 H5+6
9. P6.5
0.5 points (Answer 4)
6. P4.5 K5.6
  6. ... K5.4
7. P5+1 (Answer2)
7. P5.6
1 point for the last moves of the main line (Answer1)
Puzzle 2: Red to move and checkmate
Solution

Red's naked king wouldn't survive long, if Red's own attack would fail. Fortunately for Red, cannon, horse and pawns are co-operating well and can force the win:
1. H1+2      
2 points, threatening 2.H2-4 K5.6 3.C5.4 checkmate
1. ... C3-1
  With the idea 2.H2-4 K5.6 3.C5.4 C3.6, immediate 1. ... C3-2 gives positions similar to the main line. If Black plays P3.4 here or later, K5.4 yields positions of the main line as well. 1. ... P4.5 2.K5+1 doesn't solve Black's problems.
2. C5+1 C3-1
3. K5.4
1 point
3. ... P4.5
4. H2+4
2 points
4. ... P3.4
  4. ... P5+1
5. K4+1
5. P6+1
1 point
5. ... K5.4
6. P7.6 K4.5
7. P6.5 K5.4
8. P5.6 checkmate
1 point for the last moves of the main line (Answer1)
Puzzle 3: Red to move and checkmate
Solution

Another one of these positions where a red cannon in turn uses one of it's own pieces and the opponents advisor for a long series of checks. Black can't do anything. The problem for Red is to find the best path for his horses. Experienced problem experts will guess immediately that the red rook might have to give the final blow, but Red's horses have to work a lot before the rook can start the final attack:
1. H2+3 K5.6      
2. C1.4
1 point, Red has achieved his first goal, with the help of the horses the cannon will be able to give as many checks as necessary. Next goal is to capture Black's central pawn.
2. ... A5+6
3. H4-3 A6-5
4. H--4 A5+6
5. H4+2 A6-5
6. H2+4 A5+6
7. H4+5
1 point, second goal achieved! At the moment the horse on G8 doesn't allow Black's king to escape via E9. For the next steps this horse will be needed for other tasks, therefore Red's second horse has to control E9. For that reason this horse has to reach the palace corner D7.
7. ... A6-5
8. H5-4 A5+6
9. H4+6 A6-5
10.H6+4 A5+6
11.H4+6
2 points, next goal achieved, now the horse G8 is free. It's mission is to capture the advisor on D9!
11. ... A6-5
12.H3-4 A5+6
13.H4-3 A6-5
14.H3-4 A5+6
15.H4+2 A6-5
16.H2+4 A5+6
17.H4+3 A6-5
18.H3+4 A5+6
19.H4+6
2 points, next step is to release the pin on Red's rook. For that reason, the horse D9 has to be transferred to D2!
19. ... A6-5
20.H+-4 A5+6
21.H4-2 A6-5
22.H2-4 A5+6
23.H4-3 A6-5
24.H3-4 A5+6
25.H4-6
1 point, Red's rook is free and can start the final attack
25. ... A6-5
26.R7+8 A5-4
27.R7.6 mate
1 point for the last moves of the main line (Answer1)