Others have said much of this, but I hope to be able to expand:
1) I don't think so. I tend to think that secession is a matter of state (in the sense of a political unit, not the American sense) sovereignty and that states have an inherent right to protect their sovereignty and national authority. When a political unit seeks to secede it inherently threatens the sovereignty of the state from which it is seceding. That state is entitled to protect itself and prevent secession as a defense of its sovereignty, if it chooses. The secessionist entity is the one violating the state's sovereignty by attempting to establish its own sovereignty. From there, secession becomes a practical question. If you win, then you were justified and if you lose then you weren't. Simple enough I think. However, since World War 2, international law has moved away from this position toward extending people the legal right to secede in certain circumstances. In practice however, the old regime still applies.
2) Neither, as I don't think it is a right in the first place.
3) In theory, secession is permissible so long as the state seeking to secede requests the consent of the United States and that consent is given. However, there is absolutely no legal right for a state to secede. It is something that a state may do when the United States chooses to permit it, but the state has no intrinsic right to secede because when states joined the US they joined a perpetual union, giving up their right to certain aspects of sovereignty. Further, as already mentioned, the Supreme Court has ruled on the legal merits of unilateral secession. Namely, that they are nonexistent as states have no right to secede on their own. When they do, legally, the state is not held to have seceded, merely to have had its rightful government usurped by the secessionist authority.
There is another argument here that basically says secession is, fundamentally, a question of sovereignty which is often an extra-legal matter settled by states outside of a legal context. I.e, the Civil War showed that unilateral secession was illegal because the North held that view and won the war. Personally, I find this the most convincing view from an historical perspective, though not a legal one.
4) Nope, no formal procedure. Presumably if a state actually wanted to secede it would submit a petition of some sort to Congress in a similar manner to territories applying for statehood.
5) No. The states that formed the CSA all declared their secession independently of the formation of the Confederacy, as I understand it. They then joined together to form the new state. However, they all seceded unilaterally and therefore their actions were illegal.