This doesn't sound like it's being caused by the Intel driver at all at this point the more you go into specifics. You may have (or had) malware which when removed caused the browser issues, as well as the file association problems. The BSOD's may be from said malware, or maybe just a different issue that is coupled with the malware. You may not have or have had malware at all, and those issues are just a symptom of constant crashing. Driver updates are generally in the executable format, so I don't know why you cannot run any of them.
At this point, it may just be in your best interest considering all of the secondary issues to run a repair or clean install of Windows.