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.
Drywall mud is the thick, goopy white stuff you use to fill the seams between boards.
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, it is better caulked with a water resistant caulk. ( Also it should be at least water resistant drywall or concrete/fibre board.)
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
It shouldn't be a problem. The glue is water based and the mud should adhere to it.
Nothing
I use basic drywall primer over all of those.
lightly wipe the drywall mud after it drys
You don't put 'spackle' on at all. After taping the drywall seams you 'mud' them with drywall compound. -It is a totally different substance from 'spackle', which should be used only to fill small holes and irregularities in wall.
The white side needs to be out. If you look closely at the edge you will see a slight recess in the board. This is so you can mud and tape the joint and not have a bump at the joint.