Thailand will always live in the past. Deeply engrained xenophobic paranoia. As an example, I arrived in Singapore and went through the automated gates and it takes 15 seconds, no lines. With my passport details they can do all the required security checks instantly without a pointless arrival authorization. Last year I had a 5hr stopover in Changi. I entered and exited the country twice. Each time it took 15s and no lines at all.
Veryify the Van is going to Siem Reap and not just the border. It also may be the case there will be one van to the border and then change to another one on the Cambodia side. Maybe post again after you take your trip with an update.
It is unclear if you are taking your own vehicle or rental across the border which is why you are getting these type of responses. I don't know if there are vans from Bangkok to Siem Reap but there are big buses. However, a flight is only 2000-2500 baht which is not that much more. 100% get an e-visa in advance. The Cambodia border officers will try to overcharge. If you do decide to take one of the International buses, verify if they will accept an e-visa. Some international buses insist on having a physical Visa in your passport. Finally, a nice way to get from Cambodia to Vietnam is to travel to Phnom Penh and take the boat to Chau Doc. Visit some in the Mekong and continue to HCMC.
The Tourist Visa is valid for 90 days. Which means you can enter Thailand up to 90 days after the Visa is issued. The duration is 60 days. A 30 day extention is available. However, if you plan to travel to other neighboring countries then plan to leave before the 60 days and return on a 30 day Visa exempt entry. If you are visiting multiple neighboring countries then you could just enter Visa exempt and leave before 30 days each entry. No Visa required.
The requirements are clearly stated on the Bangkok Bank website. There are several options, one of which is a work permit. One other is a reference letter from an Embassy in Thailand. This actually is a form from Bangkok Bank you take to your Embassy who will notarize the document.
Except for a few branches that deal with foreigners, like the main branch on Silom Rd in Bangkok, most don't have any understanding of the different options and are likely to just say "need work permit". At this point ask them to contact the help desk in Bangkok who will explain to them what is required. Also, you do not need the ATM card with the useless insurance. Just the basic card for 200 or 300 baht. I opened my account on a Visa Excempt Entry.
Shouldn't cost too much for a TB patch test, Drug test and Syphilis test. About $50 total is what I paid. The Elephantiasis and Leprosy tests were not possible. The GP I went to simply did a physical exam and signed off on the form.