Answer:
If im honest im pretty weak in push-ups maybe 5 if I push myself 10-15.
To improve a vertical jump you will want to exercise your cafts and legs, for a vertical jump, I would suggest squats and squat jumps, try several things it does not necessarily haft to be an exercise set up random things to jump over, and turn to your side a bit while doing it. Stretching will help alot to, it does require some flexibility and coordination, but i'm sure you will figure it out!
Goodluck!! :)