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Hi Yes,you can paint on top of the wallpaper,as long as it’s well attached and in good condition. You’ll definitely need to use a primer and then any paint on top

you can’t beat stripping the paper and doing the job correctly; but if times a factor and as long as the paper is well stuck and no lifted edges ( if so re stick ) then yes there is no reason why you cannot emulsion over. but beware if it’s a patterned paper your dealing with you will probably see the pattern outline bleeding through the emulsion . also be aware the paper will probably bubble up when emulsion is applied but should disappear when dry. if not slit bubble with Stanley knife re glue; let it dry and repaint.

Yes you can I'd use a slightly diluted trade paint to prime the wall and leave to dry fully. Depending on how good it's attached you will possibly get bubbles under the paper which hopefully will go as the paint dries. Then paint over in a good quality paint. I would roll the paint on then layer it off with a good brush to remove the orange peel effect that rollers leave.

Advice to paint it with any emulsion is void really as you haven't supplied information as to the type of wallpaper it is. Some wallpapers are classed as paintable but most are not especially vinyls. Vinyls can be painted and i have achieved this but there are very few paints available to do this and they are not cheap. Painting finishing paper will present a lot of problems usually. The seams will lift, it will bubble etc etc. A cheap alternative would be to strip it and re-paper with a blown vinyl/anaglypta. These can be then painted with any emulsion