welcome. Also, I believe it's now possible to for you to file a TM 30 on the internet. However, I have no experience in doing this so I don't feel l should give you any advice about how to go about doing it. Maybe someone else who reads this and has experience filing online can comment and give you some guidance.
yes, the TM 30 is the form you or your landlord will file within 24 hours of changing where you live. (Note: if you move to a new apartment, house, condo on the weekend, then you are supposed to file the next day that your immigration office is open.) If you file the TM 30 in person, the receipt will be stapled in the back of your passport, just like your latest 90 day report. If you don't have a copy of the receipt, you should ask your landlord for a copy and staple it in the back of your passport. You will need a current TM 30 on file to renew your long stay visa. I believe (I'm not 100% certain about this) that the fine is 800 THB if you or your landlord fail to file the report. Immigration seems to be cracking down on this as of late. BTW, if you are on a tourist visa and staying in a hotel, you can disregard this. The hotel will take care of this for you.
if you go to the immigration office you use, they should be able to provide you with a list of items you will need specifically for "your immigration office" (they are not all the same.) I use Jomtien Immigration and I do my extensions myself, with a list provided by Jomtien Immigration. I renewed my last extension of stay at the beginning of this month. It only took me about 2 hours total and I spent 2,200 THB for the pictures, bank letter, photo copies & immigration fees and I was good for another 364 days.
American here who has tried to get my Thai WIFE a US tourist visa in the past and I've had no luck. I could move back to the US & apply for a green card for her but that would take months and honestly, neither of us want to live in the US anyway. I do not believe the odds are in your favor but I wish you good luck regardless.
Have you been sending at least 65K THB each month from outside of TL and does your bank book or bank statement reflect that each monthly deposit came from outside of TL? If yes, you may be able to switch from the 800K method to the 65K monthly deposit method or possibly a combination of the two, depending on which immigration office you use. If you've been sending the 65K go talk to the retirement desk at immigration.
it's a Thai immigration form that you must fill in and turn in as part of the 90 day reporting process. Just Google it and you should find the form and examples of how to fill it in.