If I am understanding your question, you are asking if quotation 2 and 3 are of the same format or usage, and what their name is if they are grouped together.
To answer the first part of that question, the 2 are not the same. In your first example, the quote in question is what we call a "saying." The definition of a saying is:
Any concisely written or spoken linguistic expression that is especially memorable because of its meaning.
In the case of number 2, it is a simplified way of saying something else, so it is a saying. It is put in quotes, not because you are quoting someone, but because it is a quote (confusing, I know).
With number 3, you are quoting BBC News, and you use quotations because you are directly referencing what BBC News said. You are correct when saying it is external data, so you are not guaranteeing its accuracy, but merely stating what BBC News said. This is the most literal definition of a quote, and is not the same as number 2, which is a generally quoted, but unattributed quote (meaning nobody knows where it originated, but it is still a quote, or saying).
As for the last part of your question, "...do the others have names?" I am sure there are "official" names for each of these, but if you are giving them your own names so you can better understand them, the only correct way to name them is what makes sense to you. The only one I would change to avoid confusion is number 2. You might consider naming it something more along the lines of "this is a general saying, and I am using it in place of a more literal definition." People use sayings when they want to convey a message, but they use a general saying like the one in your example so that it can apply to many different situations.