Passport stamps and visa stickers are legacy items that are not needed if flying in to a major airport.
Definitely carry hard copy of the pdf though. Land borders and regional airports still may need them.
BKK has auto gates for departure and I believe they're coming soon for arrival, which means there will be no human, or machine, looking at your visa sticker or PDF. This is not new technology either. Thailand are just catching up...
As others have said, just print a few of copies and keep them wherever you keep photocopies of your passport and other important backup documents.
You need to meet the criteria. For remote work, you need to prove employment or that you're actually engaged in work, but there is no requirement to show any actual income from that work.
No matter on what basis you apply for the DTV, there is no requirement to prove income. You definitely need to prove that you already have enough money to fund yourself. Apart from that, you also need to prove that you are engaged in remote work, or required to be in Thailand for a specific purpose, such as education, sport training, medical treatment, etc.
They basically want you to justify that you are busy with something other than working in Thailand and that you're self-sufficient.
it's a great visa, but you need to qualify for it. Unless you leave Thailand at least every 180 days, you'll need to keep proving your bank balance and Thai language course.
I you arrive in Thailand with a visa exemption, or tourist visa, you can then get an O visa in Thailand and avoid the insurance requirement.