Use drywall compound, or a 'drywall friendly' caulk like Alex ll. This is easy to apply and sets in about an hour, does not shrink in small holes and can be sanded.
Painting isn't going to cover them, it is just going to give them color. You need to mud and sand them smooth, then prime before you paint.
Cutting drywall before you snap it .
yes If you dont prime new drywall, then there is a chance that the orange peel texture maynot cover all unpainted surfaces and you may have to repaint due to the obsorbtion of the paint in the drywall. It also helps seal the surface of the new drywall and makes for a better and more uniform finish.
The poly shield goes directly onto the frame before drywall.
In the room - sweep, vaccum, dust, wipe down the walls (use a just barely damp cloth for best results. In a small area, a tack cloth is best.
Never heard of that before. The drywall may be very dusty, or the primer iwas not mixed totally.
Plastic sheeting works well for this, and yes it goes behind the drywall on exterior walls to help prevent moisture from getting to the drywall.
You want to put the tub in first.
The wall was not cleaned or primed before painting. The wall was wet before painting. The paint was not properly mixed before painting.
The best way to drywall a curved or radius corner is to wet the drywall. If possible lay the drywall over a form that matches the radius to be covered. use a garden sprayer or watering can an wet the drywall. It will bend to match the form before your eyes. Let it dry out. It will stay in that shape and will easily be applied to the curve. Tighter radii may require using a thinner drywall like 1/4". Use the same method, but apply two layers if the rest of the job is 1/2" drywall
If it's only a very small piece use Alex ll caulk, this dries to paint in about 2 hours. If it's a larger piece than a loon or dollar coin, then use wallboard mud and fibre tape.
If it is glued to the wall and the wall is drywall/sheetrock, then the paper of the drywall will come off with the mirror. Drywall/sheetrock repair will be necessary. Your best bet is to use a glaziers set of suctions cups. Buy pulling with enough pressure, the mirror will eventually break loose. It WILL damage the drywall, so either replace the mirror or the drywall. It is the mastic you are trying to break. Just before it comes loose, you will know it.