Puzzle 1 from an endgame textbook

The correct move is 1.K5.4

After 1.K5-1?? Black can win easily:
1.K5-1?? P4+1 2.P4+1 P4.5 3.K5.4 (or 3.K5.4 H4+6 followed
by H6+8 checkmate) H6-8 4.P4+1 K6.5 5.P4.5 K5.4 6.P-.6 H8+7
checkmate, Answer 1

With 1.K5.4 the game will result in a draw if both sides
play the best moves:
1.K5.4 P4.5 2.P4+1 K6.5 (but not 2. ... H6+8?? 3.K4-1 P5+1
4.P4+1 K6.5 5.P5+1 K5.4 6.P4+1 and Red wins, Answer3)
3.P4+1 H6-5 4.P5+1 K5.4 5.P4+1 H5-6 draw, Answer2

or

1.K5.4 P4.5 2.P5+1 H6-7 3.E3+1 draw, Answer4 
       

Puzzle 2 from a game HE WeiYan - HU Ming played in 1998. This
game was shown in XiangQi Review Volume VII, Number 6

The better move is 1. ... H1-3, Black can grab the pawn later.

However, the situation after 1. ... C8.4 is not as clear as
the continuation in the game may suggest. Black, apparently
in time trouble played 
1. ... C8.4 2.C8+1 C4-1?? 3.H5+7 and Red will gain a piece:
3. ... C4.2 4.H-+8 H5-3 P9+1 Answer1
Black should still have tried 2. ... C4.2 3.P9+1 H1-2 and
I don't see anything better than 4.H7+5 E7+5 5.P9.8 This endgame is
clearly better for Red but Black can still fight for the
draw. Answer2

I have to admit that 1. ... H1-3 isn't simple either. XiangQi Review
suggested 2.C8-1 C8.4 3.E5+7 H5-6 indeed yielding a drawish looking
position, Answer3
Perhaps more dangerous for Black is 1. ... H1-3 2.H5+7 2.C8.4 H-+8
Black should not underestimate the combined attack of three red pieces.
However, I can't see how Red can succeed if Black's defence is accurate.
Many different lines are possible, I'll give only one example:
1. ... H1-3 2.H5+7 C8.4 3.H-+8 H5-4 4.C8.7 H3+5 5.C7.9 H5+6 6.H8-7 C4.3
7.H-+5 H4-3 8.C9+1 P9+1 9.P9+1 C3+2 10.H7+8 H6+8 11.C9+3 C3.9
and the outcome of the game is open, Answer4.
       

Puzzle 3 from a game SUN Zhiwei - HU Ronghua

1.R2+3 is the better move.

Red played 1.P1+1 and succeeded in winning Black's cannon:
1.P1+1 R5.7 2.R2+2 R7-4 3.P1+1 E+-5 4.P1.2 P2.3 5.H6+4 R7+2
6.P2.3 but his material advantage turned out to be insufficient.
After 6. ... E5-7 7.H3-2 H1+3 (Answer1) Red did not find a win.

1.R2+3 would have yielded a clear win:
1.R2+3 E+-5 2.H6+4 R5-3 3.H4+3 R5.7 4.P1.2 and there is no
defence against Red threats with H3-5, e.g.
4. ... H1+3 5.H+-5 R7-1 6.P2.3 E3+5 7.P3+1 and Red wins, Answer2