As far as removing it. No luck just pulling it down? I didn't think so. They sell a tool called a ?paper tiger? It's round and you just run it over the paper. There are little knives that cut into the paper, but not the drywall. Once you've done that then you use a mix of ?vinegar? and water to wet the paper and it should come off. The directions on the paper tiger will be better.
But if you find that the walls were not sized or primed before the wallpaper was hung and you are tearing the face paper off of the drywall(if that is the type of walls you have) I would stop and paint over it. But if it is peeling you will to remove thoes areas and then skim out the wall with joint compound. The primer you will want to use is oil based and can either be a quick dry stain killer type or a slow dry, it just depends on how much time you have. This will pretty much make it a part of the wall.
How you remove the wallpaper depends on how well it was installed and what kind of wallpaper it is. Essentially, what you need to do is get water, soap, steam, or a product called "DIF" underneath the paper to dissolve the glue holding the paper on the wall. Some glues will dissolve with only warm water, some more with soapy water, even more with steam, and virtually all will come off with DIF.
Some wallpapers are multi-layered with a top layer that peels off, leaving a fuzzy paper layer glued to the wall that is water permeable. You probably do not need to score this paper, just soak that fuzzy layer with water, soap, steam, or DIF, and it will get through to the glue.
For papers that do not have a top layer that peels off, you need to score/perforate the paper with a Paper Tiger or scoring knife with enough holes that the DIF or water can get through to all the glue. LOTS of holes. But not so deep that the holes perforate the drywall cardboard underneath the glue.
Removing wallpaper behind cabinets requires you to remove the cabiunets. I don't see the question, there. I also don't see why you would want to do so: just keep it there.