Do all orbital flights take off in the same direction due to the rotation of the Earth?
However, satellites heading to polar orbits of course launch north or south, and famously Israel launches things into retrograde orbits, due west, because of lack of suitable launching locations that head east.
In the case of suborbital hops, it doesn't matter, because your target isn't orbital speed, and what you lose in free speed you gain back in your target coming towards you as you hop.
Flights that want to orbit over the poles take off aiming perpendicular to the rotation instead. A few satellites have been launched backwards intentionally.
P2P sub orbital hops are either direction, 30-40 minutes, maybe 25 for shorter trips like London to New York.
Low sun synchronous orbits are approximately the same as polar oribts, more perpendicular than retrograde. I'm not sure if we use high sun synchronous orbits for anything?
Majority of LEO sats are sun sync