Yes you can paint them with latex paint.
Hi, I am sorry but the answer is no. You will need to strip off the tiles from the walls first, repair/re-plaster the wall and then paint it. Applying 1 or 2 coats of paint on top you will have bad result as a many many little cracks on the paint as the 3D foam tiles are soft at the touch ad the paint once dry is solid and not flexible.
Yes you can, but just use acrylic paint on it.
Three coats of gloss polyurethane later.
Yes. You can paint the 3D self adhesive foam tiles and I recommend you to use a high quality water based paint.