Okay, I have reinstalled OSX Mountain Lion, and I will update this thread after a few hours to see how it's going. But, please read below:
In order to reinstall, I attempted to use recovery mode (held down command-R at boot). First I booted into recovery mode, then I formatted the hard drive, then I attempted to install OSX via wireless connectivity. However, the wireless stalled halfway through. Again, just like what we have been experiencing in normal desktop mode, the wireless icon showed I was connected, but data simply stopped transferring. I disconnected the wireless and reconnected (while still in recovery mode) and the OSX download seemed to pickup where it left off, but it kept happening. I became impatient with this, so I made a USB bootdisk (I used several different methods, Lion Diskmaker, Disk Utility, and even using the Apple Recovery Disk app). None of these USB boot disks would work. When I attempted to boot and hold down the option key, I could see the USB, but it would not boot from any of them. It would simply return to the prohibitory sign (like a do not enter sign) and then turn off. So then I decided to try and go back to the regular recovery mode, but because I had formatted my drive earlier, the recovery disk partition was no longer there!!! Finally, I booted into Internet Recovery Mode (command-option-R at startup). This mode downloads a recovery mode environment from Apple servers. This time, after downloading the recovery disk software from the servers (instead of using the one pre-installed on the macbook air when I got it), the internet never stopped working. The download took about an hour and never stalled.
The fact that the downloading of OSX never stalled at all after I downloaded a NEW recovery disk via the internet recovery mode (instead of using the preinstalled one) makes me think that this is actually a software issue and not a hardware issue. Perhaps it's possible that a certain amount of these machines were shipped with corrupted drivers. I simply don't know.
If you do what I did, I recommend that you first get the ethernet thunderbolt cable, because it can take a long time to download OSX over wireless, and it's possible that this is indeed a hardware issue and you will end up with a formatted computer with no way to reinstall an OS and you'll have to either go to the Apple store or mail your machine in. Again, none of the USB boot disks I made worked.
Good luck everyone, I'll update this thread later.
