I would like to redo my basement walls. All but one wall has very ugly "knotty" looking paneling and one wall is brick with a fireplace. Can I put drywall over the paneling and the brick? And how far away do I need to keep the drywall from the fireplace.? Please help!

Do not install drywall over paneling, its easily removed. You need to see and tell us what is behind the paneling. Furring strips are thin 1x2 wood boards nailed to a surface so you can nail another surface like paneling on top, not a good way to build a drywall surface.

My garage is closed in but the cement brick walls aren't . I was thinking of furring the wall and insulation with styrofoam panels. What type of finish woul be the best. I live in fla. And my walls don't sweat. It just keeps the room from getting comfortable temperature wise.

Florida is a big state, is it really hot and humid in the summer like much of the state? I'd use green board, only a few $$ more than drywall but water resistant.

I don't see why you could'nt drywall over the paneling.all conbustibles should be 2 inches from a chimney and I want to say 18 inches from the fire box.cant check right now but I will get back to you.

furring strip are pieces of 1x2 wood that are use to install drywall that do not required insulation.. If you are going to put insulation on the walls you need to use 2x4s..

There are several types of insulation that works with 1 X 2's(7/8" thick).
Spray on, Foil and Styrofoam are 3 types.
Leaving the Paneling is fuel for Bugs and fire.