Did any state have a right to leave the union?

Answer 1

No.

I believe that the issue was decided that the union was an indivisible union. Absent permission of congress a state cannot leave the union, conversely congress cannot eject a state from the union without the state's consent.

Answer 2

yes only Texas can

No, Texas cannot secede - this is a very common misconception, usually by Texans at a time when the USA are under a Democratic Presidency.

When Texas joined the Union there was a provision made for the state to be allowed to be divided in order to keep the "balance" of the states equal between north and south (think Missouri Compromise). It would be illegal for any State to secede. As Lincoln said, the USA are stronger as a United Country and not just parts.

Two points to consider. First, there's this brief history of the Lone Star State's 1845 entry into the Union, emphasis added:

When all attempts to arrive at a formal annexation treaty failed, the United States Congress passed-after much debate and only a simple majority-a Joint Resolution for Annexing Texas to the United States. Under these terms, Texas would keep both its public lands and its public debt, it would have the power to divide into four additional states "of convenient size" in the future if it so desired, and it would deliver all military, postal, and customs facilities and authority to the United States government. (Neither this joint resolution or the ordinance passed by the Republic of Texas' Annexation Convention gave Texas the right to secede.)

Second point: We fought a war over this. Lots of Americans died. The secessionists lost-including the ones in Texas. Secession is no more legal now than it was then.