You need to leveling up your Hero to increase the chances of survival in Prime Arena. Heroes level up by accumulating a certain amount of prime over time and for killing other heroes and touched . About touched you can read in another thread. The killing of other Heroes also significantly increases the Hero's leveling speed.
All abilities are available on the Q-W-E-R keys. Basic abilities are available from the get go and a hero's ultimate is unlocked at level 10. Abilities are upgraded at levels 4, 7, 13 and 16.