, That's correct, you have to apply for an extension for the same reason as your entry/initial stamp. You can change the reason for a 1-year extension when you already on 1-year extension.
Yes, it's possible if you do carefully. As you say, you need documents from two branches for next application.
BUT,
better to talk with your local immigration office before you move money. Some offices don't prefer those steps. Some don't have issue for you to do that way.
Q. can I do a one month extension on a one year non O retirement visa ?
-> No, there is no 30 days extension on Non-immigrant based visa/extension. What you can do is applying for an extension by meeting all requirements for 1-year extension, and try to ask for shorter validity.
Q. how long before it expires
-> You can apply for an extension within the last 30 days of your current stamp at most immigration offices.
Q. do I have to do it at the same time or is it ok when I just go for the extension ?
-> That depends on your current stamp. Go to the office to apply for an extension and ask when is your next 90-day report.
It's just because TTEO is NOT yet on eVisa system. They will start on 1 Jan 2025. You will apply for a visa in person at that office if within this year. Check this post.
Even if she has a reason to have to enter Thailand on a foreign passport for many times, she wouldn't have a problem as long as she can show proof of Thai nationality (passport or ID).
She can book flight with the name of either passport. Just make sure to use the correct set of the name, nationality, and passport number on the passport that is used to book a flight. As long as she has a valid Thai passport, she can enter Thailand on that. She wouldn't have issue with airline if she can show a Thai passport if it's not used for booking.
And as long as she enter Thailand on a Thai passport, it's not visa-exempt entry for foreigners as she is Thai to enter. No limit on entry to Thailand for Thai nationals.