Melodyne can be on two computers.
Melodyne Studio is the only version that ever existed with version number 3. The others stayed at 2 and went straight to 4. If you have Melodyne Studio 3 it is significantly more advanced than Essentials 4 so I'd get rid of the latter.
Rendering the clips means selecting the Melodyned clips, right clicking and selecting "bounce to clip". This finalizes all Melodyne edits and then removes Melodyne from the clip, meaning it's back to being regular audio. It's the most fail-safe way to port over projects/audio.