.

Considering this, how do I remove old thermal paste from my CPU?

Use the swab (or whatever) to wipe off the excess paste. Then use the swab moistened with iso-propyl alcohol (rubbing alcohol) to remove the film leftover. Then repeat until it is clean.

Secondly, does thermal paste expire? It depending on the solvents used in the making of the compound which may dry over the years, and not the thermal paste. This is not a reason to get stressed as the paste is still going to do its job, even when the inner substances are dry! So, there is no reason to replace the dried thermal compound.

Also know, do you have to clean off old thermal paste?

Yes, you should always remove/clean the old thermal material when changing the heatsink and apply new thermal compound(as a general practice). As previously indicated, this prevents voids/gaps/bubbles/poor seals.

How much thermal paste is too much?

Putting too much paste on a socket generally won't hurt thermal performance, because the act of tightening down the cooler squeezes out the excess. Too little paste is bad, but anything above the minimum threshold will have the same effect once the cooler is tightened down.