How does the Satellite manage to stay in earth's orbit?

It doesn't take any fuel to keep moving - there is nothing to stop it.

 

At 8km/s, if you fly through the atmosphere, probably your craft will burn

 

Newton's First Law: an object in motion will tend to stay in motion. There is no air - and therefore no air resistance - in space. Once you get the craft up to speed, it will continue on its merry way forever until it encounters something to stop or slow it (such as faint whiffs of atmosphere in low orbit.)

 

This is not relevant.

 

http://en.wikipedia.org/wiki/Newton's_cannonball

Besides the appeal to inertia that DaveC and mgb have given, the newton's cannon example is a good illustration of orbits and why the orbiting object doesn't just "fall back to earth".