As a tourist can you purchase a car whilst traveling through Thailand and surrounding countries?

For starters with a one way ticket, you will need to prove you are leaving Thailand within the time limits of your visa or entry stamp BEFORE they will let you on the airplane. And claiming you are buying a car to drive yourself out of the country will not satisfy the requirement. You will need to either get a long stay visa or buy a throw away air ticket to another country.

You can legally own a car in Thailand as a foreigner but you need to have a Non-Immigrant Visa and a Work Permit or Proof of Address Document (the later can be obtained from immigration Officials but you would need to be renting a house or apartment). If you have all this, you and the car's original owner or dealer need to fill out a bunch of paperwork to transfer the title, provide proof that you paid the annual car tax (license fee) and have paid your insurance costs for the year.

If you are buying a new car, you will initially get red license tags, which can not leave the country. You will need to hang out until the white tags are received (took about a month when we bought a new car a couple of years ago).

If you are traveling outside Thailand, you need to make sure your insurance covers you outside the country, you need to get an international license tag or sticker which has the Thai characters transposed into the Roman alphabet and you need to get a "car passport" from the Motor Vehicle Department. (you also need to carry your car title and ownership papers with you)

If you are thinking about simply selling it at the end of your journey, you can't legally sell it outside Thailand unless you get import papers and pay the duty for the country you are trying to sell it in. And don't forget, different countries here drive on different sides of the road, so a Thai car will put you, the driver, on the wrong side of the car in some countries.