b.) Death Star isn't theoretically impossible. We know you just need to direct a massive amount of energy at a planet to blow it up, the only question is figuring out how to get that kind of energy. Teleportation though, we literally have no idea how it would work or what it even means.
https://www.orionsarm.com/eg-article/4a3d78dc77e6f
You basically send your digitized DNA & personality copy to the target (needs to have reasonably high tech infrastructure already in place), where a blank body is grown & "flashed" by your personality. And voila, you are now walking the surface of another world couple light years away from your destination. (And you likely also now effectively exist at least twice, but oh well.)
There are serious ethical and security issues with this technique, but it might still be useful none the less. :)
"... a couple light years away from your transmitter"?
No I'm not, my clone is. My consciousness is right where it started, making this an extremely limited form of "travel"