Before I break the darn thing, can you tell me if the back panel comes off or if I have to unscrew the top and bottom screws?

Many remotes are different. If you worried about breaking try removing the screws.

Why doesn't the Harbor breeze remote control reduce the fan speed?

If everything else functions properly, the capacitors in the receiver are bad. Replace the receiver.

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More