Time Machine problem - Boot OSX and errors

I recently (finally) upgraded from Leopard to Snow Leopard on my Macbook Pro. Since then, I have had problems with my Time Capsule. Almost every hour when it is time for the automatic back-up, one of two possible error messages from Time Machine pops up. The message is sometimes "A volume you are backing up is case-sensitive, but the backup volume is not"; and sometimes "The identity of the backup disk has changed since the previous backup. The disk may have been replaced or erased, or someone may be trying to trick your computer into backing up to the wrong disk." When this happens, a back-up does not occur.

The strange thing is that some hours, I do not get an error message at all; instead, the Time Capsule backs up just fine. However, when it does back up, two drive icons appear on my desktop: one saying 'Boot OSX' and another saying 'Backup of [My Name]'s MacBook Pro'. On the desktop it looks like this: and in Finder, like this:

I would really appreciate any help figuring out what is causing this and how I can get Time Machine working properly again. Thank you!

 

I don't remember doing anything like that. I'm not very savvy with Macs, so I pretty much just backed up and then followed the on-screen steps when I installed Snow Leopard :/