The process can become very complicated as the rules change on a regular bases in Thailand. Speak to an attorney or your school about the latest changes in government policy. Note that in Thailand you also need a ‘Cultural Certificate’ when you wish to teach in Thailand. The following is what would normally be needed to apply for a teacher license in Thailand.
If you have a work permit in Thailand then you will need to pay income taxes. The taxes for foreigners are the same as for Thai citizens. Note that you are not allowed to hold a profession in Thailand that a Thai citizen can do. There is a list of prohibited professions in Thailand which you can view and see what you are not allowed to do while in Thailand.