I have a rough in for a basement bathroom and have a few questions...

1. If I am going to put a shower enclosure in, should I frame behind it or just have plastic moisture barrier against the concrete with the fiberglass enclosure over that?

I would frame behind it. That way you can install insulation and drywall. It will make a better looking job.
Unless you need the space and can't install framing, do what you have to do.

I should put drywall BEHIND the shower enclosure, or just around it? Thanks!

Sorry missed the fiberglass part. Install the unit to the studs then drywall around the unit to cover over the nailing flanges.
You may need to cut the back of the drywall towards the edge so the nailing flange doesn't cause the drywall to slope out.