"After December 31, 2015, the Department of State will no longer add extra visa pages to U.S. passports.
"U.S. citizens applying for passports outside of the United States will receive 52-page passport books. The 52-page passport book will cost the same as 28-page passport book would."
There's never been an extra fee for the bigger book, but automatically issuing it to Americans abroad is something they started at the beginning of 2016 when they stopped offering extra page inserts.
Just to clarify, there is no additional fee for the larger US passport book (and it is now issued automatically if you're applying overseas, but applicants in the US can get one by ticking the appropriate box on the form).
You are not on a multiple entry non-O like the OP, you're on a retirement extension and have a multiple entry reentry permit. Unlike the OP, you don't have to leave the country unless you want to. There's no fee for coming back in with a reentry permit - the OP just paid for transportation and facilitation (and presumably an entry fee for Burma) in order to get his new three month stay as quickly as possible. If you take a trip somewhere and reenter normally, Thai immigration will just stamp you in with no charge.
You're generally correct, except that deed polls aren't used in the US - they mainly exist in Commonwealth countries. But yes, the US will be fine with her using any name that reasonably describes her and that she uses habitually.
For passport purposes, the US does not require a separate legal name change procedure for applicants who get married or divorced. The marriage or divorce certificate on its own can be used as proof, and an applicant can use either the current or previous name as she wishes, if that's the one she uses in everyday life.
Her passport is not fraudulent at all. If she's American, the US State Dept has always accepted that people may use different names at different points in their lives, and specifically permits divorced citizens to continue using a married name in their passport after divorce if that is a name that they've habitually used for at least five years for other purposes.
You probably looked at something like this and overlooked the part that says "once you have your letter...". The "visa on arrival" system that they're talking about (which has basically been defunct since covid) was only for people with pre-approval letters to get a visa affixed to their passport at one of those airports - it NEVER allowed Americans to just show up without prior authorization and get a visa upon landing.