Do you have a job offer from a school? If so, most of the legitimate schools I have heard about will help you with the process, many of them practically take care of it for you.
To renew you each year you will have to show that you still are employed by that employer. You work permit and visa are tied to that employer unless you get an independent work permit - one not tied to an employer. Those are a little more rare but one of the regular posters here obtained her independent work permit as a teacher and she'll be able to tell you much more about that than I can.
If you have a job, you do not need the proof of income from outside Mexico. That is just for "rentista" status and you would have employee status.
Yes, you always need to keep INM informed of any address change.
To renew you each year you will have to show that you still are employed by that employer. You work permit and visa are tied to that employer unless you get an independent work permit - one not tied to an employer. Those are a little more rare but one of the regular posters here obtained her independent work permit as a teacher and she'll be able to tell you much more about that than I can.
If you have a job, you do not need the proof of income from outside Mexico. That is just for "rentista" status and you would have employee status.
Yes, you always need to keep INM informed of any address change.