Mavericks GUID issue and Time Machine questions?

Good evening.

First off, some system specs, to make this a little easier:

Model: MacBook, 13-inch, Aluminum, Late 2008

Processor: 2 GHz Intel Core 2 Duo

Memory: 4 GB 1067 MHz DDR3

Graphics: NVIDIA GeForce 9400M 256 MB

Software: OS X 10.8.5

NOTE: At one point, I used BootCamp to run a Windows 7 partition on this machine. Upon an unexpected shutdown from Windows one afternoon, my partition became lost and could not be retrieved. It is not shown when I go into the boot menu for selecting a partition. At this point, I have not reformatted my machine to attempt to reinstall Windows.

On to the current issue.

I recently downloaded Mavericks with the intent to install it and upgrade. After a lengthy download, I clicked through the standard agreements, and was greeted by THIS lovely error when selecting Macintosh HD.

"OS X Mavericks cannot be installed on Machintosh HD".

Alright, great. It's giving me the GUID information, but when I go to select the option to change it to GUID, I cannot select the Partition tab. It's simply not there. The drives I can select from on the left menu are as follows:

Hitachi HTS543225L9SA02 Media

disk0s2

Macintosh HD

Only the Hitachi drive gives the Partition tab. It is unavailable when I select the other drives. So, a question before I continue.

What the heck is the disk0s2?

That's one of my stumpers.

My other question is about Time Machine. I recently purchased a My Passport 1TB model and formatted it to become my Time Machine backup. I only have a vague idea as to how Time Machien works, I will admit. So another few questions.

Will Time Machine allow me to recreate my data and system from its most recent backup?

Do I have to reformat my disk before I can upgrade to Mavericks?

How do I retrieve my OS and data from Time Machine if I reformat?

I'm in strange country here, since the transitions from Leopard to Snow Leopard to Lion to Mountain Lion were flawless, but Mavericks wants to be stubborn.

Any suggestions or guidance would be a boon! I'd love to upgrade, but I don't want to lose years upon years of data thanks to user error!