Your understanding appears basically correct. Also, the kinds of mistakes you have pointed out are indeed quite common.
Note, however, that the second part of the following item is not equivalent to the first part. (I've starred the second part to indicate its incorrectness as a translation of the first part.) The first part does not imply that humans exist; instead, it implies that if they do, then some of them are not men. The second part unconditionally asserts that human beings exist who are not men, a quite different statement.
Not every human is a man. *There are human beings who are not men.
Edit: The error of equating the two parts is an example of an existential fallacy, and if there were no humans, it would be an example of a vacuous truth. The wikipedia article about existential fallacies says
The existential fallacy, or existential instantiation, is a formal fallacy. In the existential fallacy, we presuppose that a class has members when we are not supposed to do so; that is, when we should not assume existential import.
One example would be: "Everyone in the room is pretty and smart". It does not imply that there is a pretty, smart person in the room, because it does not state that there is a person in the room.
...In modern logic, the presupposition that a class has members is seen as unacceptable.
The wikipedia article about vacuous truth discusses arguments for treating none, some, or all vacuous truths as “true”. (An argument related to non-equivalence of the example sentences is that the Implies operator and the Logical AND operator are not equivalent.)
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