Well done.

V-1

1.R3h2! Bxh1
2.Rxh1 d2
3.Bxb7+ Kxb7
4.Rd1 c3
5.g6 Rc1
6.g7 c2
7.g8=Q Rb1+
8.Ka5 cxd1=Q
9.Qd5+ Kc7
10.Qc5+ Kd7
11.Qd5+ Ke7
12.Qe5+ Kf7
13.Qf5+ Kg7
14.Qg5+ Kh7
15.Qf5+ Kh6
16.Qf6

Here the black h-pawn comes in handy.It protects from escaping the black king.
There are a lot of perpetual checks. It's a draw.

V-2

1.R3h2! Bxh1
2.Rxh1 d2
3.Bxb7+ Kxb7
4.Rd1 c3
5.g6 Rc1
6.g7 c2
7.g8=Q cxd1=Q
8.Qd5+ Rc6
9.Qd7+ Kb6
10.Qd8+ Ka7
11.Qd7+ Kb6
12.Qd8+ Kb7
13.Qd7+ Rc7
14.Qd5+ Ka7
15.Qd4+ Ka8
16.Qd8+ Kb7
17.Qd5+
It's a draw.

Yes.

It's because of Rb1+.

However, before looking at the tablebase, do consider black's options after 6.g8(Q) to understand why black can win. It is important in finding the solution.

Alena, the position is los after 1.Rxh4?? You can confirm this by looking at the Nalimov Tablebase after Black's fifth move.

1.Rxh4! Bxh1
2.Bxb7+ Kxb7
3.Rxh1 d2
4.g6 Rc1
5.g7 Rxh1
6.g8=Q d1=Q
We reached the position: 6Q1/1k6/8/8/1Kp5/8/8/3q3r w - - 0 1. It's a critical position for white. Now white must be very cautious. The goal for white is to destroy the black c-pawn and give perpetual checks.The white queen must give precise checks so that the black queen couldn't protect the black king from checks.

7.Qf7+ Kc6
8.Qxc4+ Kd7
9.Qf7+ Kc6
10.Qc4+ Kd7
11.Qf7+ Kd6
12.Qf8+ Ke5
13.Qe7+ Kf5
14.Qf7+ Kg5
15.Qg7+ Kf5
16.Qf7+ Kg4
17.Qe6+ Kh4
18.Qe7+ Kh3
19.Qe3+ Kh4
20.Qe7+ Kg3
21.Qe5+ Kg2
22.Qg5+ Kh3
23.Qe3+ Kg2
24.Qg5+
It's a draw.