Just saying 'Republic' is correct (there's nothing wrong with that); that just doesn't specify that there are several layers of Republics. That's all the word 'federated' means...
This is correct as well, although redundant, as one is essentially saying the same thing twice... A Republic already IS a constitutional form of government, so to add Constitutional in front of it is redundant...
This is the most specific/accurate way to describe what the USA is. This is specifying that there are several layers of Republics within the USA (federal, state, local...)
Wrong. This is a paradox. There is no such thing. A Democracy is 'mob rule' (rule of people), while a Republic is 'constitutional rule' (rule of law [a ruling document]). A country cannot be both a Democracy and a Republic. It is one or the other...
Correct, but "democratic elections" doesn't make a country into a Democracy. "Democratic elections" can occur in Republics as well, as you have just described here... It's just a particular method of electing representatives; it has nothing to do with the form of government itself.
Yup. It means that there are several layers of Republics.
We democratically elect leaders, but that doesn't make us a Democracy. We are a Federated Republic. See the U.S. Constitution...