Can you paint over wallpaper?

Just because you can doesn't mean you should. Will make it much harder to remove the wallpaper down the line, and it eventually will need to come down. My vote is to do it right from the get go. Remove the paper, repair the walls where necessary, wash the walls, prime, then paint. The end result will be far more professional.

https://www.lowes.com/projects/paint-stain-and-wallpaper/remove-old-wallpaper/project

I wouldn't. Too many issues.

Yes, you can paint over wallpaper as long as it is not loose, damp, peeling, puckered or bubbly. If you can go to a bottom corner and check the firmness of your wallpaper, you can make a better decision about taking down the wallpaper or not. Best wishes ☺️