Indeed, four states (Virginia, North Carolina, Tennessee and Arkansas) resisted joining the Confederacy until invading union armies crossed their borders. Some of those same states went for the Constitutional Union Party (Andrew Johnson being the only southern senator who remained on the Union side) in the election of 1860. And even when Tennessee joined the Union, a number of counties in the eastern third of the state remained solidly Republican until this very day.
Wrong. Those states seceded in reaction to Lincoln calling for troops after the south fired on Ft. Sumter, and long before any US forces stepped foot into their territory. Of course, this was exactly the reason that the confederate states chose to fire on Sumter in the first place, to push the wavering states into their camp.