Emulsion paint is meant to go onto your PM project, once it has dried, BEFORE you put anything else on.  It acts as a sort of sealer to protect the pm from being adversely affected by regular painting.  After applying it, you can then continue covering your project in any way you choose.

What I'm uncertain of so far is if there is much of a difference between the 'normal' emulsion paint that you paint your walls with, and the stuff called "primer" that is put beneath it, or if it even matters for PM use.

You should be able to clean brushes with just soap and water, since emulsion is water-based.

I have never painted a house before, all I know is that "primer" is supposed to go onto your walls before the normal wall colour layer, to cover up any imperfections of the wall and make sure the second layer sticks.  But I'm guessing it doesn't matter for PM, just regular old white latex wall paint is what you need.  I'm likely completely overthinking the whole thing =P

Apply the emulsion to your project after your paper is completely dry, let it dry again, then paint it with your acrylics or however other way you wish to finish it.  The emulsion is meant to go beneath the acrylics, rather than replace them, although I don't see why you couldn't use it alone if you *really* wanted to.

I mostly use acrylics, but I've used latex, oil, and even watercolors on past PM projects with good results.  I never seem to have any problems with mixing different types of paint, but your mileage may vary.