Can my wife get a one-year extension on her Non-Immigrant ED Visa in Thailand, and can I get an extension based on our marriage?

It’s only valid for 30 days, that probably means that you have to use it within 30 days.

Make sure you bring documents with you to prove you are married

Everyone has a plan and advise for when you deal with immigration but it's not until you get there in the day that you will see if your plan works out the easy way or a more difficult route . Creative interpretation of rules creating a problem where there was none to then in turn create a solution for you .

If you got single entry Non-Immigrant type visas when you enter the country you will get stamped in for 90 days NOT 30.

When you have about 30 days left on the 90 day stamp you're going to get when you enter the country you go to the immigration office with documentation from the school your wife is studying at and they will give her a 90 day extension (there is no yearly extension for studying at private schools).

At that time you will provide documentation to show you're married and will be granted an extension for the same duration.

Once you get your extensions you can get a re-entry permit BUT remember it is only good for the current extension (90 days), so each time you get a new extension you would need to get a new re-entry permit if you are going to travel during that time