Paper-Printing Pros of YA- wtf does this description mean and does this type of paper seem okay for a cd case?

80 pound is too thick; it's more light cardboard than paper.  Between 50# and 60# (about 200gsm) is more appropriate, but sturdy paper down to about 32# is sometimes used.  The print shop should give samples for you to compare.

Good definition requires good coated paper.  With permeable paper, ink diffusion blurs text and images.  The term "Satin C" does indicate a coated product, although I'd expect to see C1S or C2S (coated one side, or two sides).  If the reverse side doesn't matter, use the cheaper C1S if you like.  Either gloss or satin should give bright colors.

You may want to use curable ink, UV-curable being the most common, which actually solidifies the ink.  Curing time is negligible, in the millisecond range or less (microseconds in industial-scale printing).  Alternatively, a combination of ink and paper that's guaranteed smear-proof should be adequate.

that would be like a card stock.

"May Bleed" doesn't sound good. My suggestion is to take an insert from a CD you do have to your local shop for comparison, no need to guess.