Bathroom vent fans must be vented to the out of doors. Venting this fan into the attic is simply asking for problems. The excessive moisture will cause condensation on the roof members, insulation and eventually cause mold. It is never OK to vent directly into an attic even if the attic itself is vented.
So, the simple correct answer is NO. Your friends are misinformed.
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.
Best Answer
This is not normal. The trim plate should be tight against the finished ceiling.
You might be able to simply push the trim plate up, where it will lock into place. If that doesn't work, you'll have to adjust the retaining clips to hold the plate in place.