A loud minority of Texans call for Independence, which is not really possible as far as I know, BUT could the Rest of the USA just kick another state (Not necessary Texas) out? Or is this also not possible?
I suppose it's possible but it would never happen unless that state basically committed an outright act of war against the rest of the US. At that point they probably would have left the US on their own though.
And even in that scenario the US government would probably send in the military to forcibly take that state back before they just give up and force them to leave.
It's not possible legally or Constitutionally; it's possible in that they can secede by amending the Constitution, or by winning a war of secession, but that's it. They can't leave and they can't be kicked out.
Though they could be divided into or amongst other, smaller States.