On Parasite's 4th click of life, he has leap/climb and 2 damage, so he can use pounce, but then can he also use steal energy with it, so he doesn't take the click of pushing?

Steal Energy is not optional and is always in use (unless outwitted). So in other words, if he does damage, he is healed a click (or rather, stays put).

Well... sort of. The push happens no matter what. However, if your Pounce victim happens to take damage from the close combat attack (the requirement for Steal Energy to work), then yes, Parasite would heal a click back, effectively negating the push.
It's important to note though - if your Pounce attack misses, or if you hit but fail to damage the target (it makes its Impervious roll), Steal Energy will not activate and Parasite will still have to take Pounce's push without any healing click.

Another note on timing: If you're on Parasite's last click and try the Pounce/S.E. thing and damage your target, the S.E. healing click would happen first (it activates when the target is dealt damage), then Pounce's push would occur afterward (it activates after the action is resolved). So last click Pounce is good to go with S.E. (if you think you have a good chance of hitting and damaging your target with Parasite's 6 attack value).