1) Significantly.
2) Yes, thermal paste is actually a good insulator. Both surfaces need to be flat, apply a modest layer of paste to both sides, and then scrape off the excess with a straight edge (like a razorblade). Just remember the thermal paste serves one and only one purpose and that's to eliminate air gaps.
3) The element probably is small those little fridges aren't generally designed very well. Not sure how to go about determine it's cooling power though. Keep in mind the biggest limiting factor is ambient temperature and keeping the hot side of the element as cool as possible, otherwise you can't pump heat from the cold side.
4) Peltiers efficiency is usually pretty low. They've gotten better but not dramatically so, and again they're still highly limited by their ambient air conditions.
5) No idea what that stuff is, I find it on mosfets frequently, wish I knew what it was myself, and where to get sheets of it.