Is my terminology for proteins correct?
1) I don't think so. I would not assume functionality.

2) People may diverge a bit on the semantics, but here's what I would say (my background is more cell bio and structural bio than biochem or genetics).


Active - Has enzymatic or signalling activity (or some other functional capability). Often proteins have multiple activities, or different active sites, so activity should be with respect to a specific function.
Functional - I interpret this to mean has all of its native activities intact. (I don't take this to mean anything structurally). One could also use this as a synonym for active, especially for a specific functionality.
Native - I take this to mean the protein has not been altered from its form found in nature. This implies it is functional.
Mature - My natural feeling for this is that it means the protein is structurally mature, i.e. it has been folded properly, transported to the correct cellular compartment, post-translational modifications completed, etc... For a non-functional mutant protein, I would hesitate to call it mature though, even if it were not semantically incorrect.
Stable - I interpret this entirely structurally. i.e whether the protein has folded to an energetic minimum or their natural structural state (incl. proteins with disordered domains). People might say, though, that stable means it has a natural lifetime, i.e. the cellular environment or the enzymes present are not destroying it at an abnormal rate.


I'm not quite sure what (3) is asking; if you edit, maybe I can comment.