1) Yea, sorry, turbofan, not turboprop nor a jet.

2) It stays burned, but the energy is banked in potential energy of the aircraft, namely in a form of altitude. If you run out of fuel 5 feet above ground, you dont get to fly far. When you run out of fuel 35000 feet above ground, you can still choose where to land from multiple options.

3) huh? I dont get what you trying to say, but: Its always more economical to climb, and the faster the better. Ofc you cant climb too high when you intend to attempt to land in 5-10 mins, but nontheless, every feet gained is "banked", and the aircraft is more economical to run the higher you are.

4) I am not saying the winds arent a factor, and in no way I was arguing about how fuel reserves are calculated. My only claim is that: yes, by spending more fuel to gain altitude, you can then "glide" down almost for free later. Its not 1:1, because of constant losses like drag, but its being compensated by higher engine efficiency and less drag at altitude, that its always worth it to climb if you can.

There was a flight that was low on fuel diverting to alternate between 2 islands. The pilot panicked and chose slower climb to intuitively save fuel. They had to ditch the plane in water because of it - if they initiated full climb, they would have made the jump.