Can you texturize walls that have wallpaper on them and then paint or do you need to remove the wallpaper first?
Removing the wallpaper is best. Some of the wallpaper might come loose while applying the texture and painting. But if removing the wallpaper involves tearing up the walls surface to do it then leaving it in place will work. What might happen when applying the texture and painting is bubbles.
Primer will help prevent bubbles and give the texture something to stick too. The best primer for wallpaper is either tinted shellac or stain killing oil base like Kilz. You can use a good acrylic primer instead, but this could cause some of the wallpaper to bubble. Bubbles will have to be cut out, the area primed then spackled before applying the texture.