I rise and fall as boats stall over mountain ridges and trolls fidges stone by stone built up in rome just to fall back down in london

I am a word of letters five. Remove my first, and I am an energy that keeps you warm. Remove my second, and I am a place where things are kept. Remove my third, and I am a word used to signify a choice.

I cover a nut I cover a plane I keep you afloat I keep you intact in outer space I’m actually quite common place

I cover you fully, yet shed when renewed, A canvas for ink, or a map poorly viewed. Burn me in sun, or I'll peel in disgrace, Without me you'd slip. I'm your flexible face.

What starts with a P, ends with an E, and has thousands of letters? Anwer is two Words connected, E ReadingRoom, not Reading room.