CC won't let me mix and match clothing bottoms and tops. If I use a bikini top, for example, if I use any bottoms other than that product's bikini bottoms, like a skirt or something, the top disappears. If I try to use pantyhose, the top disappears. Is this a glitch, or is it something wrong on my part?

There are numbered clothing layers for your character. If both layers have the same number, it will replace the old layer.
Go to Conform and highlight the cloth you want to change the order of. Hit the gear icon to access the cloth layer settings.
I think this should help you. God Bless.

O wow! I didn't know that, thanks so much! You're very helpful.