I know nothing about the situation with German tax but the broad principle is that if you are a Thai tax resident and bring income into Thailand then you are liable to pay Thai tax on that income. If the country the income comes from has a dual tax treaty with Thailand then you can claim a pro rata tax credit against any tax already paid on that income
it's a basic principle of tourist entries that they are convertible to other visa types but of course you must be eligible to apply for those other visa types
If you want to work inside Thailand you will need to get off the DTV and onto a visa such as a Non-B that allows you to do so. The good news is that the DTV is basically a tourist visa so you are allowed to convert to another visa type inside Thailand
if you plan to work remotely from inside Thailand you really only have to visa options. The DTV or the LTR Remote Worker visa. A marriage visa is probably irrelevant