If you show up at a US port of entry without any sort of anything the default decision is to deny entry (exceptions for Canadian citizens and citizens of a few small islands). If you show up at a US port of entry with an ESTA/visa you will most likely be allowed entry. Refusals are relatively rare.

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.

Not for airlines and international cruise ships with US as destination. The attendants won't let you board unless you have a valid US visas. Carriers get fined if they transport individuals with no proper documents to a US port of entry.

In practice if you have the VISA they will almost always admit you. If you are rejected it generally means they find something at the border.