under what category will you apply? The first person (adult) applies and once they have been granted their DTV the others apply using their DTV reference number. Each person needs their own application for a DTV including babies
of course it's seen as work, have you bothered to look up the legal definition of work in Thailand? The DTV only mentions work prohibited to emphasise that it does not allow you to take a job in Thailand. Embassies are not the most reliable sources of information but I do agree that nobody knows what you are doing sitting in your own house, but if you are working without the appropriate visa you do need to keep it quiet.
Anonymous participant EOR services are nothing to do with working remotely, they are about employing people in Thailand. You only have 2 options to legally work remotely, the DTV or the LTR Remote Worker and the requirements for the latter are very high. If you are purely evaluating the benefits of a DTV over a marriage visa there aren't many that I can see
you seem confused. You don't need to report within 24 hours, the owner of where you stay must do the report, which it sounds like they have done already
attached. Is this the visa you applied for? This what is known as the Non-O visa, its a 90 day visa which you then extend for 12 months inside Thailand
if only 1 child will get an ED visa then only 1 parent can get a guardian visa. Other than getting a job and associated work permit (not straightforward) your options are going to be limited to a DTV visa, an ED visa but you will need to study and attend school, or if you have enough money perhaps a Thai Privilege. You can let the kids not studying just overstay until they are 15 with no repercussions other than getting overstay stamps, although I don't recommend this. You could add them as dependants for the DTV