No, it will almost certainly loosen the wallpaper.
Some wall papers need to be coated before you can skim over them with drywall mud. Check with you local Sherwin williams.
It shouldn't be a problem. The glue is water based and the mud should adhere to it.
when you hang drywall, you have to tape off the seams with paper tape and "mud", then "float" the mud smooth. the drywall float is a flat metal tool on a handle that you drag across the mud to smooth it out, like when you smooth out the icing on a cake
I use basic drywall primer over all of those.
Usually, there is drywall under the wallpaper. It is not difficult to remove the wallpaper (by steaming, or another method) to get to the basic drywall. Then, you can texture it and then paint it.
No, you plaster or mud it first.
To fix a ceiling that was spackled with drywall mud instead of spackle you can use sand paper to scrub it. I don't understand why you have a problem with it. That's quite common. you normally just paint primer over it. Using sand paper to scrub it is going to be extremely dusty.
If it's small spread mesh tape over it, then mud it. If bigger than doorknob size, put a patch of drywall into it then mesh tape and mud.
Sheetrock is primarily gypsum, combined with sand and water.
Almost anything you do WILL take off the top layer of paint and possibly drywall paper so be prepared to recover it with mud and sand it down.
If by wall board you are referring to drywall (aka gyprock or plasterboard) then you use drywall mud and tape in the usual manner. If however you are referring to paneling, then it is a different matter.
If it is just a small amount, cut it with a craft knife with the blade almost parallel to the drywall. You will have to mud over the cut.