Hi, this seems to be a very simple question but I can't find the answer anywhere!

Here's my current (possibly flawed) understaning of centripetal/centrifugal forces:

Newton's First law states that a body remains at rest or travels in a straight line unless an unbalanced force acts on it. So to make a body travel in a curve a force must act to pull the body away from its straight line.

The force that pulls an object out of a straight line path into a circular orbit is the centripetal force (centre seeking). It is the force on the orbiting object. From Newton's Third Law if a force acts on an object then there must be an equal and opposite force acting on another body known as the centrifugal force (centre fleeing).

Stone on a string whirled around your head- the force acting on the stone is the centripetal force, the force acting on the hand is the centrifugal (centripetal and centrifugal force is the same thing but depends on your point of view-from the hand or from the stone?).

So, satellites.

An artificial satellite in orbit around the Earth experiences a centripetal force exerted by the gravitational pull of the Earth on the satellite.
What's the centrifugal force here? I've been confusing myself by thinking about the velocity of the satellite which keeps the satellite from being pulled back to the surface of the Earth but I know this doesn't make sense.

Newton's Third Law means that the centrifugal acts on the Earth. So is the centrifugal force the gravtitational pull of the satellite on the Earth?

If anyone can answer this question and/or point out the misconceptions in the above, I'd be eternally grateful!