Stewie: For the two-month rental, I would think it would be much simpler to rent a car rather than buy one. I sort of get the desire to drive an old T-bird across the country
, but it seems like a ton of paperwork, hassle, expense, etc....not to mention the risk that your classic car breaks down or otherwise needs work in the middle of nowhere. Thunderbird has had "good" eras (where it was a true American classic) and "bad" eras (where it was a piece of junk).
Long-range month-long point-to-point rentals are probably not cheap, so you might have to fine-tune the itinerary a bit (say, a circle trip for a portion of it instead of straight point-to-point). But this seems lower risk and eliminates pretty much all of the issues related to foreign residency and insurance.
Omar: in the U.S., the car will have state-minimum coverage on it from the rental agency. Liability cover. You'll need to provide cover for the value of the car plus potentially other coverage. Honestly, on a one-day rental as a foreign national, the easiest thing to do is just buy the cover that Dollar will offer you at the counter. It will be, statistically, a notorious rip-off - something like $25 per day. But unless your home insurance company or credit card provides out-of-the-box coverage on U.S. rental cars, it's probably the easiest thing.
You should not have any issues renting the car. Foreign nationals rent in Hawaii all the time. My own personal experiences renting in Europe as a U.S. national are that I occasionally have difficulty explaining my own insurance. That's why on a one-day rental I probably wouldn't buy some online policy from a third party. I'd just pay Dollar (or whomever). If you were talking about a week, then I'd say it's worth more investigation.
Also note that if you rent a highly unusual car, many standard out-of-the-box coverage (like from your credit card) don't apply. Something to consider if that first link is actually renting Hummers.