It doesn't matter if it's completed in time. When you apply for a marriage extension you get an "under consideration stamp" which is a temporary permission to stay in Thailand until your extension is processed. Normally it's about 1 month for marriage extension.
You can apply for a marriage extension until the last day of your existing permission stamp. Then your consideration period allows you to stay until they complete processing your extension application.
A multiple re-entry would not help you. The visa only gives you 3 months when you enter Thailand. Getting multiple re-entry will not change that your permission to stay in Thailand only lasts for 3 months. You need to get a 1-year extension and the re-entry permit on that if you want it for long term.
a visa does not guarantee you entry into a country. A visa just dictates how many days you'll receive if you're allowed to enter. Entry is at the discretion of the immigration officer, same as every country.
If you entered on visa exempt and then got a new passport, you can still apply for an extension. They will check your old passport and want copies of your entry stamp from that passport, but the extension will go into your new passport.
Each bank branch sets their own requirements for opening a bank account. You would need to go to a bank branch and try to open an account to see what they require. Many will require a certificate of residence from immigration as your proof of address. If that's the case, then what the bank requires doesn't matter, it's what your immigration office will accept as proof of your address. Each immigration office sets their own requirements, so you would need to check with your immigration office to see what they require for a certificate of residence.
Wise should be fine to transfer the money, and make sure you choose the correct transfer option for living in Thailand long-term so they will attempt to make it look like an international transfer.
International is not a requirement for retirement extension, but it might be beneficial in the future regardless.
A tourist means if you are admitted to Thailand, you will receive a 60 day stamp based on your visa. There are recent reports of people being pulled out of line after entering on a METV and then leaving and returning and interrogated about why they are returning so soon as a tourist. Tourist entries (whether they are visas, or visa exempt) are not intended for long-term living in Thailand.