HD size inconsistency

Hello,

I don't really know how to start this thread. I have had a high number of problems with my computer, which I suspect to have been somewhat related to one another. I've seen the Genius bar many times too, although not for this specific problem. So right now, my computer is having some "difficulties" evaluating the total amount of space used and available on the hard drive. Here are all the specs I think I need to say:

MacBook Pro 15-inch, Mid 2010

Mac OS X 10.7.5

DiskWave, Version 0.3.0 (0.3.0.179)

Problems I've been having (random listing) and things I've done because of that (beside the one of this question's topic

- computer heats to "burning" temperatures, "burning" as in "my skin cells are being destroyed"

- frequent freezes

- makes me do frequent disk reapirs by rebooting using Disk Utility (holding alt when rebooting)

- computer seldomly functions very slowly (nothing's opened, nothing's connected, but for 2 hours, the computer will just run extremely slowly)

- trash can't be emptied, or is taking absurdly long (problem I'm having as I'm writing this now)

- makes me relaunch finder, and ... try to empty the trash again until it succeeds.

- I shut it down once and the fans didn't want to stop, I had class so I put the computer in the sleeve. I take it out after an hour and it smells burnt. The computer is burning hot.

- computer generally runs slower than computers with same specs from friends.

Repairs and comments by Genius bar:

- changed the HD and cable

- didn't find anything wrong at every of the 3-4 tests they run throughout a year. They still recognized the computer was behaving weirdly and abnormally slow.

- I did many disk repairs, and a few reinstallations. When they changed the hard drive, I transferred all my documents, folder by folder, testing the computer speed by transferring a 1GB file from an external disk to hard drive, this between each folder move. No changes.

- I frequently clean up my computer with CleanMyMac

Picture 1 is just an interesting bug that appeared and disappeared 3 days ago.

Picture 2,3 and 4 were taking within the same minute. As you can see, everything kind of disagree. Summing up DiskWave individual folders gives the 193.26GB that Get Info says are available, but DiskWave and About This Mac say that there's only 81.66GB available. About This Mac says that 111.6GB are taken up by Backups. I have a Time Machine back-up disk, but it wasn't connected while I took these screenshots (and they're 500GB anyways). So why are there 111.6GB of backups, and why don't they appear on the hard drive?

Please feel free to help me on any of the problem I've listed above: I haven't posted about any of them yet. They're too random for me to explain very well anyways.

Thanks!

Julian