Your visa states "employment prohibited". The Thai authorities permit online work, but I wouldn't go around advertising you're working in Thailand as that can lead to misunderstandings and problems.
You'll only need to prove what you're doing if you go in for an extension, but you can always use an alternative such as a soft power activity if you're no longer employed.
I'd imagine a work contract you update and having the 500K in your account for at least 1 month would suffice though; you can easily update a work contract yourself even for a company you no longer work for.
Since we're talking work based abroad, Thai authorities really have no way of verifying anything.
Tax returns asked for at consulates. Can't see it being asked for at immigration in Thailand when entering the country. No way for immigration to verify its authenticity or to deal with lots of different languages.
That's good advice but not practical for most. You only need 500K to apply for the visa and to receive an extension not as an ongoing thing or for entry or re-entry. The documents needed to apply are also generally not needed; verbal confirmation of what you do should normally suffice (it has for me).
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.