When is evidence like marriage certificate, banking details, and pension payments required for a Thai marriage visa application?

The online Visa that Brandon explained lasts for 90 days once you are in Thailand. Therefore you have about 3 weeks to open your Thai bank account and deposit the 400,000 baht, so that you can apply for the extension of stay before your visa expires. Good luck.

Everything is checked every time. They are all BRAND NEW applications.

First you apply for the visa from the embassy, and meet whatever requirements they have. Each embassy sets their own requirements so you need to see what your embassy wants.

Then when you arrive in Thailand, you will be applying for the extension from immigration. This is a brand new application, and will require everything that your immigration office requires. Each immigration office sets their own requirements so you should go to your immigration office ahead of time and ask them for the handout of requirements for a marriage extension. If using 400,000 baht, the money will need to be in a Thai bank account in your name only at this point, and must have been in the account for 2 months already at the time you apply.