AIS, 200B p/m unlimited data, got it on Thai airways. Registered it at AIS shop in Patong during sandbox (Jungceylon). Good service, decent data speeds, streams Netflix no problem.
I have the same visa, I opened a Kasikorn Bank account, ATM card, bank book, banking app. Needed a Thai address (no mail goes there) and also my UK address. I opened it in Sukhumvit. Documents passport, driving licence, visa.
My only comment would be that July/August is the start of the rainy season. If you want to come to Thailand do it, ignore a lot of comments they're generally biased one way or another and personally i'd imagine a lot of things will be returning to some kind of normality by then.
Mine was the same as yours (see attached image). It was authorised, no need to change language or anything else complicated. Call your insurance company to change the wording on the cover note.