That cylinder I'm assuming is chrome or whatever finish your valve is. It will unscrew from the brass body, or there may be a locking ring (unlikely). It sounds like one of the washers in the valve got pushed out of place, which could also be the cause of your banging problem, as when the faucets aren't sealed, they can vibrate.
Here's a video showing the disassembly, there are some other links from this page.
How To Repair a Tub-and-Shower Valve | eHow.com
I think your assessment is correct, but depending on the kind of diverter you have, there should be no difference in temperature between the spigot and shower head, as the diverter should be after the mixer.