Be sure to scroll down... there may be more than one question on this page!
Partially dried spackle is... partially dried. This is the equivalent of adding sand to fresh spackle. It loses some of it's strength and smoothing ability, and if the holes are more than tiny... screw holes, picture hanger holes... it may not even hold in the wall.
I am not a big fan of old-time spackle. It doesn't work "off the knife" very well and it dries very hard. This was fine when all the walls were plaster, but today's softer walls of paper-faced drywall do better with a softer, more easily sandable filler. So instead of plain old spackle, get a container of the newer lightweight spackle. It is a relatively dry product that is very workable, and dries so quickly you can paint over it within a half hour under normal circumstances. In fact, you can paint over it immediately with latex paints if you find a very small hole, such as a nail or picture hanger hole, as you are painting!
You can definitely paint over wallpaper, but I have mixed feelings about it. First, the seams will show through the paint unless you carefully coat them with a skim coat of wallboard compound to hide them. Second, you must use an oil based primer to seal the paper, or the latex paint could cause the wallpaper paste to soften, causing the paper to "bubble". Another "hidden" problem is that many wallpapers have a texture... sometimes not very noticeable until painted. Flowers, anyone?
Even if the paper is vinyl (which generally does not let water through) it is wise to prime because using a good oil-based primer-sealer will insure that the paint will stick to smooth vinyl surface.
The reason I don't suggest painting over wallpaper is that if the wallpaper begins to fail, the walls will begin to look very ragged. The repair is not difficult… simply cut out all the loose areas and smooth them with wallboard compound. Since wallpaper failure tends to be progressive, this process of failure/repair will continue on and on over the years. If you spend the time now to strip the paper, you save yourself future disappointment.
Once you paint, the removal process becomes much more tedious and difficult, since the paint has removed any porosity in the paper and also stiffens it by adding more thickness to the wall. The more coats of paint, the worse it gets!
Nowadays, with the high quality chemical wallpaper strippers available, removing wallpaper is not as much of a chore as you might think. Messy, yes, but not catastrophic. I have an article at the site that discusses some of the issues in wallpaper stripping.
It is always difficult, and sometimes impossible, to remove painted-over wallpaper without damaging the walls... especially if your walls are wallboard or a similar product. Plaster walls can take more moisture abuse and can stand more abuse. That is why the number one choice is to just leave it on the walls. With the proper repairs, all but the most awful wall surfaces can be restored to their original smooth glory!
The general procedure is to cut out all loose areas of paper and level the walls with wallboard compound, as if you were fixing shallow holes. You can similarly cut back loose seams and fill them. Once you do all the repairs, a coat of an oil-based primer is required to seal the walls. If you use a water-based primer, you may cause more of the wallpaper to release where you don't want it to! Also, though water-based primers have really improved over the last 20 years, they still tend to dissolve stains and carry them to the surface of the paint, leading to possible bleed through into your finish coat.
Removal of the paper is another more serious and more difficult task. Paste dissolving chemicals and/or a steam wallpaper remover will be your tools of choice in this endeavor. Of course, for the chemicals or steam to get to the adhesive beneath the paint/paper collage, you must somehow mechanically pierce the paint film. One old-time method is to use a stiff wire brush to abrade the surface of the paint and paper. Fast forward to the 20th Century… there is a retail product called the Paper Tiger that does this a little more neatly and easily. The Paper Tiger is a small hand-held tool that has hundreds of small pins attached to wheels. Rolling it over the surface of the wall introduces hundreds of small holes, usually deep enough to penetrate the surface but no so deep that you will require extensive wall repair afterwards. This product is commonly available at paint stores. The only drawback is that it may not fully penetrate through multiple layers of paint.
One you have sufficiently scored the paint film or paper, you can begin stripping the paper. You have two options. You can use a chemical wallpaper stripper, available at any paint or hardware store, which is mixed with hot water and sprayed on the surface of the wall. The chemical dissolves the paste and helps lift the paper from the wall. Your second, more severe option is to use a steam wallpaper stripper. Many paint stores and rental centers have these available, and will provide instruction in their use.
If the above methods fail you, the final and least desirable method would be to use a chemical paint stripper. Because these products are very toxic and possibly damaging to many other surfaces (including your body), I list this as a last resort when other less dangerous remedies have been ruled out!
I have seen wallpaper applied over raw, unpainted wallboard many times in both private homes and condominiums. The most commonly used technical term for this timesaving contractor technique is CHEAP. Other widely used terms are LAZY, INCOMPETENT, and UNPROFESSIONAL. The builder may have saved a few dollars, but the homeowner pays dearly for this breach of trust... trust that the contractor had done the job right.
You must use either a wallpaper steamer or chemical stripper to remove the paper. Either method may damage the wallboard surface, especially if you have to make intense use of a scraper to remove the paper. Once you get the paper off, your job has only just begun. Now you have to repair all the damage done to the surface of the wallboard to give you a smooth surface for either wallpapering or painting. Even if you were to "texture" the walls, some preliminary smoothing will be necessary unless you were going to use a very heavy stucco-like texture.
Have you considered the possibility of not removing the wallpaper at all? If the wallpaper is well stuck and doesn't have a textured surface that might appear through the paint (big embossed jungle flowers are my favorite), you can prime the paper with an oil-based primer. This will seal the wallpaper so that the moisture from water-based paints or patching compounds will not loosen it or cause it to "bubble". Any loose areas or imperfections should be cut out prior to priming. This is especially true of the seams... even the slightest looseness will cause later attempts to hide the seams (read on) to fail. So trim back the seams to where there the paper is absolutely solid.
Seams can be a problem because they will show through the paint unless given special treatment. Prime all the wallpaper first. Then apply a few thin coats of wallboard compound to the seams just as if they were taped wallboard joints, tapering the coating out at least 10" on either side of the seam. This will thoroughly mask the seams making them virtually invisible.
Once all the miscellaneous repairs and seam repairs are sanded smooth, prime the repairs alone or (if it's easier) prime the entire surface again. Then you are ready to paint the walls with the paint of your choice. Proper sealing will ensure that your job will last!
Some vinyl wallpapers can be very difficult to remove. The reason is that the surface of the vinyl is nonporous. This is fabulous in kitchens and bathrooms... vinyl's resistance to water and chemicals allows it to be cleaned and, with some heavy vinyl's, scrubbed!
Alas, this quality is a two-edged sword, especially when wallpaper removal time arrives. The same nonporous quality you valued earlier becomes a curse! Many vinyl papers are called "strippable", meaning you can lift a corner and the vinyl will easily pull apart from a lighter paper backing. The backing is porous and application of wallpaper stripper makes cleanup a snap. There are unfortunately some papers, like yours, that will not pull off without a little gentle assistance.
In a nutshell, you need to perforate the surface of the vinyl to allow the stripping chemical to get through it. This can be accomplished in two ways. You can purchase a special tool designed for this job, called the Paper Tiger ( I had to look the name up... I had a mental "skip" and became fixated on the name "Wallpaper Weasel" but, after some reflection realized that was probably some wallpaperer's nickname!) This device, available at virtually all paint stores, perforates the paper in random patterns as you roll it over the wall surface.
The second, less high-tech but effective method is to use a stiff wire brush and scratch through the surface of the vinyl. Be careful not do dig too deep or you may have more wall repairs to do later!
With either method, you may have to soak the face of the vinyl a number of times for the stripper to work. Be patient and you'll eventually be rewarded!