Is there a way to see how many games you have won and how many you have lost?

Ranked games, yes. Click on your name. It's on your profile:

Completed 119 ranked games (19 / 119)

1v1: 2 / 4 (50%)
3 player FFA: 3 / 6 (50%)
4 player FFA: 1 / 5 (20%)
5 player FFA: 0 / 1 (0%)
6 player FFA: 1 / 2 (50%)
7 player FFA: 0 / 1 (0%)
8 player FFA: 1 / 2 (50%)
9 player FFA: 4 / 72 (6%)
18 player FFA: 0 / 1 (0%)
19 player FFA: 0 / 1 (0%)
20 player FFA: 0 / 7 (0%)
21 player FFA: 1 / 4 (25%)
24 player FFA: 0 / 1 (0%)
29 player FFA: 0 / 1 (0%)
32 player FFA: 0 / 2 (0%)
40 player FFA: 0 / 1 (0%)
2v2: 0 / 2 (0%)
3v3: 6 / 6 (100%)