Sealing the vapor barrier
You'll want to seal the vapor barrier to the fan housing using an acoustic sealant like OSI® SC-170™, or similar product (you might have to do this from above). Just make sure the sealant is approved for use with vapor barrier, some sealants won't adhere well to the vapor barrier.
If there is enough plastic to lap up the side of the housing about an inch, this will be a simple task. Fold the plastic back away from the housing, apply a bead of sealant around the housing, then push the plastic into the sealant.
If there isn't enough plastic to attach to the fan, you'll have to make a gasket. Simply cut a square of plastic larger than the fan housing, then make a cutout that will fit the fan. Leave the excess from your cutout attached, so you can attach the plastic to the housing. Use housewrap tape to attach the gasket to the existing vapor barrier, then follow the steps above to seal the plastic to the fan housing.
Patching the drywall
Depending on the size of the gap surrounding the fan, you'll have to use different approaches to fill it.
Very small gap
If the gap is really small; as in the drywall basically touches the sides of the fan housing, you're done. Just put the fans face trim on, and enjoy. If you really want to, you could run a bead of silicone caulk around the housing.
Small gap
If the gap is ~1" or less, you should be able to easily fill it with joint compound. It might take a few coats to fill the gap, since you don't want to put it on really thick or it will take a long time to dry. Once the gap is filled, feather the compound out to blend with the surrounding wall. You can use a 10"-12" taping knife for this.
Medium gap
Once you have a gap ~1"-2", it's time to start thinking about making the hole larger and patching it with another piece of drywall. You might be able to fill the gap with joint compound, but it will be much more difficult than with smaller gaps.
Large gap
If the gap is larger than 2", you're going to have to make the hole bigger before you can make it smaller. Cut out a square of drywall around the fan, until you get to the center of a joist on each side of the fan. Cut a new piece of drywall to fit the hole you just made, then cut out a hole in this piece to fit your fan housing. Make sure the hole for the fan is very close to the outside dimensions of the fan housing, so you'll end up with a very small gap. Tape and mud the joints, prime, and paint. Finally, follow the steps above from the "Very Small Gap" section.
You should be able to find ground screws at any home improvement store. Most boxes have a tapped hole for this purpose. If yours does not, you should be able to find grounding clips at the home improvement store as well.
Keep in mind, however, that continuity does not equal an adequate ground. Just because you have continuity between two of the boxes, does not mean you have an adequate ground all the way back to the grounding electrode. For example, the boxes might have armored cable running between them. Armored cable is only rated as a grounding conductor, if there's an internal grounding strip (which is not always the case). Armored cable could/should connect the boxes in such a way, that a continuity test would pass but does not provide a proper ground.
If you don't have an adequate ground; or you're not sure if you do or not, the best bet is to not connect the grounding terminal of the GFCI to the box. You should also place the "No Equipment Ground" sticker on the receptacle, but this is often neglected in residential situations.
Best Answer
Sure, but it won't do anything. The term "ground" implies an electrical connection to the Earth, which is normally provided by the bare grounded conductor.