how can I remove the nails from thin particle board panels?

You'll need a pair of pliers and a putty knife. Pry the nails up by sliding the putty knife between the panel and the piece it is nailed to right next to the nail. Once you've gotten the nail pried up enough to grip with the pliers use them to remove the nail completely.

try to pry the panels away from the furniture -- some slight movement will then allow you use pliers to get those tiny nails out without breaking the panels ... == THIS is a slow process and one nail at a time use a screwdriver flat blade to pry at about 1/4th inch away from the nail .....ANYWAY if you cannot save the panels then just buy a wall panel and cut it up to replace the backing of the desk ....

Your cheapest way is to use standard fiberglass insulation. You should also use baffles at the ends to allow for air circulation and be sure that you don't compress the insulation to tight against the roof. It will case the roof to rot as well as lower the effectiveness of the insulation.

One thought. Could I use a punch and drive them all the way through?

they usually use ring shank nails in that junk, so, duckrabbits got your more probable alternative. punch them in, don't pull them out!!