do you have a bachelors degree? If you don't its going to be difficult to get a teaching position, TEFL is not enough. What the right visa is depends on your situation. If you want to come and teach you will first need to find a job and get your employer to provide the paperwork for you to apply for a Non-B visa
If you apply using money in a joint account your going to need double the money in any case. Thailand views joint accounts as being only 50% yours. If the money is in an account solely in the name of the applicant its possible for them to get a visa based on 800k baht and depending where you apply the other person "might" be able to get a dependent visa for no additional cost, but this is difficult. If one were to apply for the Non-OA visa it's a bit easier but still not guaranteed
Immigration office specific. My immigration office matches my 90 day report with the expiry of my extension so the last one is normally less than 90 days. An easy way to tell is if they put a slip in your passport when getting your extension with the date your next extension is due. If they didn't then its 90 days from your last report
Nobody can give you a yes or a no. It will be entirely up to the immigration officer you will stand in front of. What I would suggest is you find a border bounce company and see if they will take you, they won't do so unless they can get you back in. It sounds like it's time for you to start looking for a long term visa though