You can stretch a Non-OA to two years by doing a border bounce just before it expires as long as you have insurance for the 2nd year. That is then finished. You either return home for a new Non-OA or get the 12 month extension in Thailand but you still need insurance and meet other requirements such as 800k in a Thai bank account.
That is not a Tourist Visa, it is a Visa on Arrival and purchased at the airport for 2000B before the Immigration desk. You can purchase any travel insurance you want.