In my last post I dealt with the Air Force question. Same argument for Veterans Affairs and the Coast Guard. The State Department just formalizes the President's grant of power over foreign affairs. The FAA is probably justified by the Interstate Commerce clause, but that's a stretch. It could be handled privately, and I'd prefer that.
I think the FBI originally flowed from the power given to Congress under the prohibition amendment (number 18). The amendment said: "Section 2. The Congress and the several states shall have concurrent power to enforce this article by appropriate legislation." It's obsolete now, and with the repeal of prohibition it's probably Unconstitutional; but I suspect it's too late to do much about it.
What you said in the beginning of this thread is that Article I, Section 8 is the limit of congressional powers, and funding a separate branch of the military called "Air Force" is not included. Neither is a Department of Homeland Security, which controls the Coast Guard. Nor is funding a State Department or the rest. What your prior post did was make the case that there are implied powers, powers necessary to govern the country. And your point seems to be that only implied powers you agree with are valid.