not at all, in my experience - depends on the country. F.e. US visas are usually valid for 3y, could be way past the passport’s expiration date, while Schengen ones are usually issued with the expiration date not exceeding the passport’s
I’ve been using visas in expired passports for decades. You have to transfer Thai visas like Non-O/B/PE/SE to new passports, but it doesn’t affect validity. With DTV which is most times is stickerless, you won’t have to do anything, most likely
Signed letter is not equivalent to TM30 in any shape or form. What you need is a screenshot from the online registration system.
Did you check in more than a week ago? That stupid online system only allows you to go back one week or so. They probably reported your stay as required, but can’t produce evidence
The easiest way to do it is to fire you and switch to contract-based employment. I know lots of people working for multinational companies headquartered in Germany and everyone based outside Germany (EU, US, Ukraine, Russia, Brazil, you name it) are on "freelancer"/"consultant" contracts (working full time, some people have been working like that for more than a decade)