Can I plaster and paint over wallpaper?
With a fresh utility knife blade cut through the wall paper around the area you wish to repair. It can be any shape, but give yourself some margin, say a few inches away from the edge of the brittled or cracked areas.

Shmoo shapes are best. (What's a Shmoo you ask?)

Within that area peel off the wall paper and anything that comes with it. Make sure you don't peel outside the area, and re-cut as needed.
Perform drywall repairs with proper backing as needed (drywall board on wooden backing, or mud on backing etc.., depending what's behind the hole)
Patch and smooth with a finishing drywall compound and feather lightly into the existing painted area. Sand as needed.
Prime and paint.

Textures may not match.
If you need more tips on the plastering / mudding part, let us know. Compounds come in different packaging (bags, tubs) and types (setting vs drying), and some are better for this task than others.