Yep established artists do as well but at that level there's more risk involved and a better understanding of what's really off limits. Like seeing an artist sell prints of Marvel's X-Men while employed at DC would probably raise a bunch of legal issues and is obviously unprofessional. Then again, their own art probably gets more attention so it doesn't make much sense to spend much effort on other things.
An example of fan art I like is Takato Yamamoto and Yoji Shinkawa's Raiden from Metal Gear Solid 2:

Yamamoto (fan art version)

Shinkawa (original designer)
Both are top level illustrators but I believe a simple agreement was made between the two artists in this case. Apart from that, the two interpretations are completely different but you can recognize who did what on the style alone.
I hope you do find a way to make fan art without worrying about copyright monsters and at the same time I hope your own style is recognizable regardless of the character you're drawing 