4 Answers

I would lift old flooring. A few reasons why. Putting laminate on top could make it very bouncy as you effectively have 2 layers of underlay. Cutting off doors as you are raising the height, how will this look against skirting boards? Are they high enough to still "look the part"? I would suggest ripping up the floor, use old underlay and save some pennies on buying new underlay!

Should be OK, best to roughen up surface of old laminate with coarse sandpaper first.

Probably bubble up like crazy.-- Can't you remove the old??

If you are talking countertop laminate, yes you can, just insure that it is down securely, and not lacking bonding to the substrate material.  Clean it with the suggested solvent, and use adhesive as directed, install as if it is over a regular substrate.  I have done it, also, I have put floor tile over vinyl flooring, no problem, also put bamboo flooring over hard vinyl-asbestos tile, gluing bamboo over it, no problems at all...