The answer to your second question could only be speculative. The convention is that wars between states that recognize one another's existence as independent states don't call their wars civil as they're not part of the same polity. This is only a convention, though.

As to your first: Congress never declared war on the Confederacy. The United States waged a war against it, of course. Congress passed articles of war and even set up a committee to examine its conduct. But declarations of war are traditionally exchanged between states which recognize one another's separate existence.

From the point of view of the United States, there was no legal Confederate state and so no Confederate diplomatic corps with which to interact, because secession was illegal, unconstitutional, and consequently null and void. They may as well have passed bills outlawing dawn or the clouds. For all the bluster to the contrary that secession was a legal, peaceful process to which every state had an absolute, unassailable right, few Southern whites appear to have believed any differently. The minority who did were largely of the old nullification school. They insisted their position was the one and only one endorsed by the Founders (The surviving founder didn't agree at all.) but really developed their novel theories in the 1820s and 1830s. It's the intellectual machinery operating in the Nullification Crisis. Which was also about saving slavery, incidentally.

You can make an argument that there's a reasonable Constitutional interpretation that supports a right to secession, just as you can make the argument for the same opposing secession. I think the latter is very much stronger, at least for unilateral secession as practiced in 1860-1, but they are both interpretations. You're not going to find black letter law saying "secession a-ok!" or "secession, no way!" in the antebellum record.

Contrary to what you sometimes hear from neo-Confederates, it was not by any stretch a matter that everyone agreed secession was legal until that Devil Lincoln and his Republicans decided otherwise. Anti-secessionist writing is abundant in both parties and both sections before the war, if not to the same degree. Southern secessionists spent a long time promoting their theories, something that the rest of the United States had little call to bother with. There are cases where the shoes are on the other feet, but I'm not aware of northern secession talk ever getting close to being a popular movement or program of action rather than a style of protest. In my field, it's largely confined to very radical and somewhat self-marginalized abolitionists.

Most Confederates who cared about such things likely (we don't have polls and their postwar accounts of their conduct are obviously a bit suspect) understood secession as a revolutionary right rather than a kind of legal enactment or universal principle (except as the right of revolution) to which one would appeal and expect a higher authority to step in and ensure compliance. A revolutionary right is one you get to exercise if you win the revolution, not the kind of thing you'd have a traditional court case over. Some advised against trying that in the secession conventions. They lost their war, so they got to be traitors instead.

But a war was waged and the obvious question from all of this is by what reasoning did the United States resist secession by force of arms. There are multiple arguments for this, some stronger than others, but the big one is that the Confederacy engaged in an insurrection. Congress has the power from right here, Article 1, Section 8:

To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;

Since the secession's not legal and setting up your own army and government is pretty obviously insurrection, it's hard to imagine a case where this wouldn't apply. The Confederate states could disagree, but they absented themselves from the Congress by the same acts that brought the question before it so they can hardly complain that they didn't get a vote. They chose to hazard a war, and indeed expected that they would fight one. They expected it would end quickly with their victory. (The United States also expected a quick victory.) James Chesnut, South Carolina's senator and Mary's husband, offered to personally drink all the blood shed in the struggle. Obviously, things did not go to plan.

Sources

Ellis' The Union At Risk and Freehling's Prelude to Civil War and Road to Disunion (both volumes) deal with the theoretical and, in Freehling's case, practical dimensions.

McPherson's Battle Cry of Freedom has all the basics.

Stampp, Kenneth M. "The Concept of a Perpetual Union." The Journal of American History 65.1 (1978): 5-33. Web. (Actual citation since I can get it off JSTOR.) Stampp is interested in establishing the plausibility of a secessionist reading of the Constitution, possibly to his detriment, but he is right on the central point that we're talking about interpretations.

Varon's Disunion! is helpful for pointing out the ways that threats of secession were used without apparent intent to follow through, though she concludes before the main event.