As their parent, you can absolutely be harassed by immigration officers when attempting to leave the country. It happened to me when my son was 6, and a nasty officer kept demanding 10,000 baht cash and tried to prevent us from getting through immigration and onto our plane. If a representative from Bangkok Airways hadn't been standing on the other side of the turnstiles waiting to RUN with us to our gate, I don't know what would have happened. I should also mention that I had my son's completed visa paperwork with me, ready to get his visa from the Thai Embassy in the U.S.
International schools require you to have a RELEVANT degree. For example, to teach elementary, you need a degree in elementary education. To teach high school English, you need an English degree. Most schools won't even look at your CV unless you have teaching experience or, at the very least, student teaching or an internship completed.
I've lived in Thailand for 12 years and haven't managed to "pick up" much Thai, like some people say they do. As others have said, it's not much of an issue, at least in the main tourist hubs, where most people speak some level of English, or will at least laugh with you as you try to speak in Thenglish or by gestures. There's always translator apps you can use on your phone in a language emergency.
The Philippines is NOT a good choice. The number of hours you're expected to work there is extreme, and I've heard many cases of teachers just not getting paid.
Best to sell your Lamborghini and buy a Toyota when you arrive (by plane). Even if you manage to get your Lambo here, getting repairs for it will be a freakin' nightmare. Maybe if you live in Bangkok it won't be so bad, but I live in Chiang Mai and have a Malaysian car, and any time something goes wrong with it, I have to wait for parts to arrive from Malaysia, and there's only a few shops in town that will even attempt repairs on it. It's horrible!
I'm not an expert on cat viruses, but every so often I hear of viruses taking out stray cat populations, so that's what I'm going off of. Obviously, vets can do the usual vaccinations here, but I don't know why anyone would risk their pet cat comingling with the large stray populations.