As for the Google for example it is same as when I was working for a Japanese company. I worked for the local legal entity and thus needed a Work Permit in Thailand. No matter that 99% of my work was global in nature ie for outside of Thailand.
It would be the Ministry of Labour where you ask if a Work Permit is required for "X" type of work. When people are arrested for working without a WP Immigration are present as they are part of the "Royal Thai Police" and thus have powers of arrest.
You are not allowed to work for a Thai company or organisation though. For that you need a different visa and if working in Thailand then a Work Permit too. Why not give some examples of the type of work you are talking about. If you are visiting Thai businesses touting for work you are working locally in Thailand and would need a Work Permit.
Depends on the local immigration office rules. As an example Jomtien said last year that must reregister after overseas trip. I did last October. Next overseas trip in February went to office and told no need. Been overseas again and since completed both renewal and 90 day report. Nothing said about no reregistering after being overseas in April
That video was with the MFA (Ministry of Foreign Affairs) and not The Royal Thai Immigration Police if you are referring to the one with the Canadian guy above.