Assuming you are on extension of stay based on working you should just be able to change the reason for your extension but will need to cancel the work permit
Bebbieluu depending on what assessable income you bring into Thailand you will need to file and pay any Thai tax due. If the country where you otherwise pay tax has a dual tax agreement with Thailand you can claim a credit for any tax already paid on that income against Thai tax as part of the process
Nobody can tell you that without a lot more information. Nationality, ages of all, purpose of visit and so on. Start by researching the appropriate visa options on the Thai evisa website
I would say if all you are doing is FIFO for work you are to all intentents and purposes living in Thailand and are not a tourist. In my view immigration are correct to tell you to get a visa appropriate for that