With regards to the DS being able to use a hyperdrive. I am stunned that people think it wouldn’t. Space is really, really big…I mean, really big. For the DS to not be able to fly at lightspeed would render it completely useless for striking fear into the galaxy.
Of course it realisticly needs a hyperdrive, but I’m not sure if that was the original intent. In the older Superman comics stuff was always just drifting from Krypton to earth with no propulsion at all more less a hyperdrive. Writers didn’t always think that stuff through, and Lucas probably didn’t either.
The Death Star is treated the same way a villain in an action movie is treated - realistically they need to be running at full speed to catch up with our fleeing protagonist, but somehow they manage to catch up while walking at a slow, menacing pace.