Can it be placed over wood paneling?

Yes. Use the adhesive that is recommended for this application that fits into a caulking gun. Don't rely on double sided tape - the tiles will just fall off willy-nilly.

I don't know of any reason why not, I would buy one sheet and just hold it up to it to see if there are any problems. We had to take ours off once and it left quite a lot of liquid glue on the back along with some of the paper from the drywall but in replacing it back on, we had no problem at all.

That is a great question! The wall to which you plan to install backsplash panels to needs to be freshly cleaned, free from dust, grease, wax, etc. After you’ve cleaned the wall, be sure that it is dried thoroughly. Acceptable substrates are drywall, plaster or clean, smooth tile (glazed, porcelain type tile; not porous or textured). Fill cracks and irregularities with wallboard compound or spackling, then sand smooth with fine-grade sandpaper. Any porous material like highly textured drywall, plywood (or any raw wood without primer), and wallpaper unless removed, sanded and primed, will result in adhesive failure.