correct, there is no visa on arrival in Vietnam anymore. You, as a Brit, gets a 45 day visa exempt entry to Vietnam. Most countries need to have either a visa in their passport or the evisa approved before being allowed on the plane to Vietnam at the airport.
you apply on the official website and pay USD 25, or USD 50 if multiple entry 90 days, get approved, print out, give that to immigration officer and get stamped in. No further money required, or letters, unless you've gone through an agent and been fleeced.
US nationals need an e-visa to enter mainland Vietnam. They don't need any kind of visa to enter Phu Quoc provided that they arrive directly from overseas.
US nationals require a visa to enter mainland Vietnam. They don't require one to enter Phu Quoc provided they enter directly from overseas and leave to go overseas.
But you have to enter Phu Quoc from overseas and leave Phu Quoc to go overseas - you can't go from Phu Quoc to mainland Vietnam unless you have an e-visa already as a US national.