Can I use Proof of Income or a foreign bank account for the Non-O visa requirements in Thailand, and do these apply to my wife as well?

You potentially can get the Non-O visa in your home country and show funds in your home country for that but it will only be good for 90 days in Thailand then you need to get an extension which will either require 800k baht in a Thai bank or an income affidavit from your embassy if they still provide one, many don't. Your wife can piggy back on yours as a dependant but they won't issue her a visa inside Thailand, she would have to travel to a nearby country that issues that once you are on an extension of stay. She might however be able to get that in your home country at the same time as you get a Non-O for retirement. Visa wise that's the easiest, banking wise the most difficult as you don't have much time to open a bank account, the money has to be in the account 2 full months before you apply for an extension, and leaving it till the last minute is a terrible idea

Depends on the country you are from. The American Embassy no longer provides an Affadavit to verify your income. Therefore you have to bank the money in a Thai bank. 800k baht for a retirement visa.