Can I apply peel and stick tile over wallpaper?

Not an expert here, but if the stuff is already not adhering to the wall without lots of help, I would not think that adding any other weight to it would be a good idea. You need some sort of a firm foundation to build on, or the whole thing is going to slip off.

I wouldn't. The weight of the tiles will eventually pull down the wallpaper. best to scrape off the paper before tiling.

Well, Yes they could be, if the surface is smooth, otherwise you will possibly be able to see the Staple outline under the tiles. Try 1 tile and see????

Yes, you can but it will probably show the staples through if they protrude! Why not test out over a staple and see.......................before committing to the whole project.............

I would not. It has already started coming off, hence staples and glued. Adding grout ( which is moist) will pull the rest of the paper off, including your tile.

The wallpaper would have to be stuck to the wall securely, otherwise the weight of the tile will peel off with the wallpaper.

Get a paper tiger tool and remove the old wallpaper with some Downey and water in a spray bottle. That mixture will take off the old glue and you can start a fresh new wall. Prep is everthing when it comes to tiling.