You can convert the DTV to another visa type at your local immigration office as long as you fulfill all the criteria for the visa you want to convert to
no. Your current visa exempt will finish as you exit Thailand and you get a new one on your return. If you are nowhere near your 60 day limit it won't be seen as a border run
In that case either you try to enter on your own and see what happens or you try a safe entry service. I don't see what other options you have other than applying for a proper visa
If you've been denied entry then who knows how long you might need to wait. A ling time if you haven't gone back to your home country. You could try contacting one of the safe entry providers and see if they can get you in, but if they can it will cost