All,

If a ship starts it's maneuver on a obstacle (asteroid) after it landed on the obstacle in a previous turn and its template does not clear a huge ship base in the next maneuver, aka the template does not allow the large ship to pass over the huge ship which is adjacent to the obstacle, does the large ship need to roll a die for hitting the huge ship AND hitting the obstacle because it is still on the obstacle at the end of turn since it could not clear the huge ship base?

Don't Huge ships remove obstacles after they run them over?

The huge ship has not hit the obstacle. It will pass right by it.

Oh, the large ship started on the rock. Learn to read, Draco.

Yes, the ship in question would suffer both the effects of overlapping the Huge ship and overlapping the obstacle.