Yes, if trying to leave and return visa exempt, this was the requirement before the new enforcement began. I don't know what it's like at those borders at the moment.
Also the news reported that if you enter via land border, you are not eligible for any extension.
No, it's not. Going home for a few months is a meaningful amount of time. Anything less than a month just looks like someone trying to get a new 60 day stamp.
I doubt you're on any visa. You are most likely on an extension based on being over 50, which is not a visa, it's an extension. When you purchase a re-enter permit, the end date of the permit is the same end date of your extension. You must be back in Thailand before your extension ends to apply for your next extension, or you must start over.
You'll need your Thai wife to attend immigration with you, along with proof of your marriage that's registered in Thailand. Some immigration offices might start the extension the day you apply, and some might add it to the end of your entry stamp. This is a generic list of requirements, as each immigration office sets their own requirements.
Do note: not every immigration office offers the 60 day visiting Thai family extension.
Because 90% of the people that book classes for soft power are never even going to see that school, let alone attend a single class. And some of the classes are only like 4-5 classes across 6 months, which hardly necessitates a 5 year visa. This is the reason many people think things will tighten up at some point, like requiring proof of ongoing courses or attendance when re-entering after the first 180 days.