Some people do border runs because they want to visit another country before coming back to Thailand, or maybe they've already extended their stay as much as possible and need to leave in order to apply for a new visa that suits their situation. There are actually a lot of different reasons. sometimes the local extension isn’t an option or doesn’t fit what someone needs.
Honestly, getting a US tourist visa seems like it’s all about luck. I got denied twice, even though I had 500k in my bank account, but I did get approved for a fiancé visa. I’ve also heard from some friends who got the tourist visa that having well-written plans for the trip really helps, but I’m not totally sure.
Yes, kids can attend international schools. In my experience in Bangkok, the school didn’t even ask for a visa during enrollment. so it’s best to check with the school to make sure you’re following the rules.
The easiest way is to have your employer help you obtain a work permit and visa. Most international schools that pay well are actually looking for teachers who have a degree in education. Wishing you the best of luck!