The house I am considering buying, most of the ceilings and walls are cracked. The house has been moved from its original location, this is a stick built home not a modular. If I have the ceilings and walls fixed will they crack again due to settling?

How long has the house been sitting on its new foundation? Most cracks happen during the first two springs seasons and settle down after that. Patching cracks is more than joint compound. You need to clean the crack with a knife and then apply a wet strip of fiberglass tape, they make a wider version if the crack is large.

When applying the fiberglass tape, do you mud the cracks first? I have cracks in old walls that I'd like to fix as well. Do you mud, then tape over the cracks with the tape, and then mud again, then finish?

Buchholtz, this should be a new question on a separate post but no, you apply the fiberglass dry and then mud over it. If your were doing seams with paper tape you'd put down mud first and then imbed the tape but fiberglass has its own adhesive. Usually do 3 coats for cracks. I use a 45 minute drymix mud for the first 2 coats and then the redi-mix for the final. Finish with a damp sponge not sand paper.