That's correct, I assumed they'd secede via some mutual agreement. You're correct in that if some state decided to leave on its own there would be a shooting match with the US and the State would lose. I have no doubt about why most guardsmen join being mostly mercenary, still, that doesn't imply much loyalty to the US over the State. Absent a shooting match with the US, I suspect most would be fine staying with the state rather than the Feds.
Not really true, the US is a true federal system with sovereignty shared between the states and the Feds. There are literally things the feds are not allowed to do. That balance of power has definitely moved towards the feds but the States still do have some sovereignty.
https://www.law.cornell.edu/wex/federalism
An example of how US States share sovereignty.
https://en.wikipedia.org/wiki/Apostille_Convention#Gallery_of_apostilles_by_state
If you note, the gallery, most of the apostilles are issued by national governments, in the US they are issued by the States.
In effect, the Constitution is a treaty between the States.
Edit to add, Germany and the UK are both good examples of federal systems as the states actually retain a lot more power than many people realize. Scotland has its own parliament after all. This is in fact what federalism means, a group of States give up some but not all of there sovereignty to a central authority.