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.