Replacement of Ventra Bath Fan
The casing is more than likely nailed or screwed to the ceiling joist on the side that does not move. It may be possible to open a small slot along the face of the joist. Then run a reciprocating saw (Sawzall) along the face of the joist, eventually cutting the attachment fasteners and freeing the casing.

The risk here is you could damage other things attached to the joist, such as wiring. If that happens, you'll need to do the alternative approach. Partly to access the fasteners and partly to repair the damage.

The alternative approach is cut out a big enough panel in the ceiling to give you room to work and remove the fasteners anchoring the casing. Patching the hole isn't too much work, though matching the texture finish can be tricky. You may have to settle for a less than perfect match.

If grounding is at all possible, such as bonding to a nearby metal cold water pipe, it should be done. However you are not required to retrofit a grounding system to your house to replace one fan. If there is no reasonable grounding means, leave it unattached.