You have to get a letter from your school stating your last day of study. Then you take that to the immigration office about a week before that date. They will cancel your extension and re-stamp you in until the date on the letter. So you can cancel it ahead of time.
There is no requirement to stay out any amount of time by air, but you're likely to be denied entry if you try entering Thailand by air after having an education visa. Immigration know it's the most abused visa type, that people use to just live in Thailand and don't care about studying. If you just spent a year in Thailand on an ED visa and then leave and immediately return without a visa, they are going to pull you out of line, interrogate you for 1-2 hours, and probably deny entry for not having a visa and trying to live in Thailand.
No. What's your plan if they call you for an interview or request proof of location again, a common thing from embassies in SE Asia to prevent exactly this.
First of all, if you're currently on an Education extension, you need to cancel that at the immigration office that issued it. If you don't cancel it, there's a chance they won't even let you leave at that border because you're legally required to cancel it, per the documents you signed when you obtained it.
Second of all, if you're entering Thailand visa exempt, without a visa, you'll need to stay 1-2 nights in Laos. It depends on how they feel at the border that day. But the days of leaving and returning immediately are over at Nong Khai and many other Laos borders. The only way to do that is with an agent.
ACH transfer from my primary bank. Pretty much every ATM is owned by a bank, at least every one that I've ever used overseas. I've always had my ATM fees refunded in Korea, Japan, Thailand.
the embassy doesn't need it to show your birthdate. That's nonsensical. No bank in the world has that. That would be an immense security breach since that's part of the security of your account.