I've done 3 houses in Pergo, and a couple smaller jobs and touch ups as well. It's great stuff, VERY easy to install (just watch the video, take the class, and take it slow). I personally always take up the old floor, but only because levelling is much better on bare floor than on any other surface. If you choose to leave it down make sure you use a high quality moisture barrier. Don't use any detergents, there's no need. Almost everything comes up with just plain water and a quick rub/mop. If anything tougher gets on it, there's some Pergo formulated remover that works great without damaging the Pergo or the glue.
As for the vinyl, it depends how old it is, what it was put down with, and what's underneath. Go to a local Home Depot, they're the fountain of all building knowledge...just take what they say with a grain of salt if there advice involves purchasing any 'special tool' from them.
Good luck, it's great stuff.