It states regarding a visa: "A visa allows a foreign citizen to travel to a U.S. port-of-entry (generally an airport) and request permission to enter the United States. A visa does not guarantee entry into the United States.
The Department of Homeland Security (DHS), U.S. Customs and Border Protection (CBP) officials at the port-of-entry have authority to permit or deny admission to the United States. "
That's incorrect, holding a B1/B2 US visa only allows you to arrive at the port of entry, the actual permission to enter the country is always left to the border officer interviewing you
Commercial carriers such as airlines are also not allowed to transport people who need ESTAs/visas and do not have them to the US, so in practice it's relatively difficult to even get to the port of entry without a visa.
The visa is immaterial to the fine unless it conveys something beyond merely allowing you to present at a port of entry, which is allowed to basically everyone.
Nope
It's the same deal as you mention above