wouldn't one of the biggest distinctions here be your "influence actions that apply in the country they are working"? an individual on DTV in Thailand is unlikely to be setting policy for the company interacting in the local Thai economy, and for 99.99% of cases that isn't be done period. I assume your situation was fairly different.
I'm quite skeptical of that. Your personal residence doesn't establish a business one, and you're already barred from doing work within the Thai economy - for your company or not. I doubt this establishes a company presence anywhere.
I wouldn't think so if your company has no presence in Thailand. If it does, then at least in other countries, they might not actually grant a similar visa. You have it regardless anyway at this point. Note this doesn't change your personal tax obligation either though.
education visas needed to be for accredited schools, I only ever heard of language, cooking, and muay thai. I'm not sure if DTV soft power needs to be accredited or not. if this has never been an option though, that may be the reason why.