The math is pretty intuitive; every second you're burning is another 9.8 m/s of delta V you have to spend counteracting gravity instead of slowing the craft down (minus air friction) so minimizing deceleration time cuts your fuel expenditure massively. It also means you have to carry less fuel so you weigh less and you spend less fuel for the same acceleration. It's the inverse of the rocket equation really, less mass is easier to slow down and you waste less energy (ie fuel mass) decelerating faster.

The higher the thrust, the lower the gravity losses. Gravity losses go down as you approach orbital speed but they aren't zero until you're in orbit. And when boosting out of orbit, the higher you are the less benefit you get from the Oberth Effect, so you want to do the burn before you rise too much, which implies sufficient thrust.

Exactly. In addition, by delaying the relight as long as possible you're giving drag as much time as possible to do the work for you (assuming you're not at terminal velocity, so not applicable for the ship.)