Is it unconstitutional for a state to secede from the union?

Answer 1

No.

At least as far as the original thirteen states, and probably those later formed from territory which made up the US at the start - basically everything east of the Mississippi. A different answer might apply to states created from the Louisiana purchase, since this was land the entire people had bought and paid for, and also to the states created from territory won from Mexico in the Mexican War, also common property of the nation.

The Constitution is silent on the issue. It neither says states can secede or that they cannot. But the idea of the Constitution was that it created a central government of limited powers, having only those powers specifically given to it by the words of the Constitution, and no more. Therefore, since the Constitution does not say states cannot secede, they may, without Constitutional hindrance.

It had taken the voluntary consent of each of the original thirteen states to enter the new Union, and everyone believed that a state could get out of it if they wanted out. Secession was talked about early on, even while Washington was president. The "back country" states of Ohio, Kentucky and Tennessee depended on the Mississippi as an outlet for their trade, and the mouth of the Mississippi was in Spanish hands, so they could get nothing to market. There were no roads to the east, over the mountains, and dissatisfaction over this caused talk of secession in the back country.

The northeastern states talked secession in the late 1790s.

During the War of 1812, the New England States were so opposed to the War that they went so far as to call a Convention at Hartford, Connecticut in 1815 for the purpose of seceding from the Union. By the time the Convention met the War had ended, so the idea went nowhere.

But, since the Civil War, no one has seriously proposed secession, and it probably could not happen today. Even though the Constitution has not been amended to outlaw secession, the Civil War pretty much settled the question. It also basically killed the concept of a central government of limited powers, as specifically called for by the 9th and 10 Amendments, which are still right there in the Bill of Rights. But the history of the US since the War is one of ever-increasing Federal power, at the expense of the states and the people.