No. On a visa exemption you have to show proof of outbound travel to the airline. They can usually see it already if you've booked an onward or round-trip ticket with their airline.
Immigration is already stopping people though. That level of entitlement won't get you across the border. Many DTV holders have been asked to step aside and provide certain documents in order to pass the borders. Some have been asked for employment contracts, details of a soft power activity, accommodation/lodging booking and/or made to sign a form.
It's becoming more difficult. It used to be possible to live in Thailand on visa exemptions, now you have to pay a visa run agency to do that, but without making pre-arrangements life is becoming more difficult for individuals who choose not to get a proper visa.
No, you're confused. The T.8 form asks you to upload your yellow fever certificate in electronic form. You will be REFUSED boarding if you are beginning your journey from a yellow fever region. This new rule was strengthened in August of last year.
No ifs or buts about it. It was all over the news.
So to fly to Thailand from one of those 45 countries, proof of yellow fever vaccination is MANDATORY.
There may be ways of getting around it; by flying on separate tickets via Vietnam or Europe or something, but if you insist on flying direct (with a transit in somewhere like Dubai) proof is needed. In fact, it may be required just to get to Dubai!