So far as I understand the question, my answer is "no" (to both clauses). And I do not think that answer is at all surprising either. As is the case with any justification of anything, one could ask for a justification of the justification, and at some point, you must either hit a wall or fall forever into an infinite justification regress. (Why does 2 + 2 = 4? Well, because it follows from the concepts of a unit, addition, and identity. Why should something "follow" like that? Logic. Why should I accept logic? Well, it just makes sense, doesn't it?) Personally, I don't know of anyone who has opted for the infinite fall. If you want to function as a thinking human being, you simply must accept at some point that there are some things you will never be able to prove; the consensus seems to be that logic in the general sense (or, at the least, some set of "first principles" that will include propositions about logic) is that "ground level" - that thing that just has to be accepted.
Now, I might be able to give you a better answer about certain formulations of logic: every logician (as far as I know) who defends or proposes a rule of logic undertakes at some point to explain why his formulation is true - see Aristotle's logic, for example. Such explanations often appeal to intuition, which is more or less just a sophisticated bet that no reader, once he or she understands the author, will be able to imagine an objection or counterexample.