You do not need proof of onward travel. But for your visa application, it may ask your intended dates of travel, so you'll need to give them an arrival date and a departure date within 180 days of arrival since the DTV only grants 180 days stay.
I'm going to assume you don't have any visa at all, and actually have visa exempt. You can get a single 30-day extension from your local immigration office. You would need to travel there and apply. The cost is 1900 baht, and you must attend in person (so an agent will not be of much benefit).
Umm, where is it that you saw that you need to get a blood test for a drivers license? You actually think they give a blood test to everyone getting a drivers license?
One of the requirements is a medical certificate. Costs like 100-200 baht and normally filled out by the front desk secretary at a clinic and not even a doctor or nurse.
Everything is checked every time. They are all BRAND NEW applications.
First you apply for the visa from the embassy, and meet whatever requirements they have. Each embassy sets their own requirements so you need to see what your embassy wants.
Then when you arrive in Thailand, you will be applying for the extension from immigration. This is a brand new application, and will require everything that your immigration office requires. Each immigration office sets their own requirements so you should go to your immigration office ahead of time and ask them for the handout of requirements for a marriage extension. If using 400,000 baht, the money will need to be in a Thai bank account in your name only at this point, and must have been in the account for 2 months already at the time you apply.