Yes you can. Residence certificate needed. Go to Land Transport Office or satellite ask for relevant paperwork ahead of time, just makes things easier. Copy sellers ID and green book.
Looking at your stamp, you have to leave every 90 days. So I'm guessing you have an evisa of some kind.This is probably the difficulty you are having. I opened a bank account on this visa last year at Bangkok Bank in Pattaya.
Yes he can get a residence certificate with TM30 whilst on visa exemption, certainly here in Pattaya, I think Krabi should be the same. If he wants to be 100% legal he would have to take a motorcycle test here in Thailand.
Best bet is apply for METV in your own country before you travel, this gives you upto 9 months here in Thailand. While you are here you can research your options firsthand for a longer stay visa.
The ask:thailand community, consisting of multiple Q/A groups with over 100,000 members, powers this platform. It is not an official government resource. Our members actively contribute to this resource, and while we strive for accuracy, we cannot guarantee its complete reliability. Assistance to travelers is provided as a community service.