Here was a similar question a few weeks ago. Try and find the thread. When I had to cancel a retirement visa as I was offered a job years ago only the immigration office who issued it could cancel it. Immigration does not issue DTV though.
From other comments many have stated their letter from employer stated specifically they were allowed to work remotely from Thailand. It probably depends on the particular embassy you apply to. As for moving from Ed to DTV others have done it and I do not think the MFA are checking that you have been working illegally in Thailand
I can assure you the process for Retirement Visa is easier than DTV if you apply in Thailand. You can always change if you wish though but if you want to do any work remotely in Thailand the DTV is the way to go.
I am pretty certain people have got the DTV teaching online to students outside of Thailand. A guy I know teaches Vietnamese and Japanese. The Viets in the evening and Japanese businessmen 5am to 7am Thai time. Free all day after that till evening classes.