It's somewhat tough, but, yes, that plastic ring is what holds it in.  I cut a
piece of aluminum stock to make a spanner tool to catch on the 'cogs' of the
ring.  You can also use a large slip jaw wrench, I guess.

With luck you'll be able to repair the sender unit.  Clean the contacts and
check with your ohm meter that it runs smoothly from 250 ohms (full) to 10
ohms (empty)

You are supposed to replace the rubber gasket when you reassemble.

Frank

You can take the fuel sender out by crossing 2 big screwdrivers and you will
see that one of
the thin black wires to the potentiometer has broken. This just needs to be
resoldered on.
This is quite a common problem with the E36 fuel sender units.

From Clive

You guessed right. The right side sender unit is an integral part of the
fuel pump, and thus it costs much more. Just your luck, I suppose ...

HINT
When my car had this problem, I was able to correct it with Contact Cleaner
and a business card. Use the business card as sort of sand paper along with
the contact cleaner to clean the contacts of the sending unit.

PS
I used a 1/4 inch Long Extension from my socket wrench set as a driver, and
gave it a couple of whacks with my hammer. There is a rubber gasket that you
want to take care not to screw up ...