If I kill the pilot of a ship like the Constellation, will the ship continue the last action of the pilot? So if the pilot was going forward, will the ship not stop by itself just because the pilot is dead, and continue to go forward?

It depends on the state of the ship when you kill them. If it wasn't decoupled, basically it stopped receiving additional inputs, but because of the way coupled works, it basically expects that you're giving continuous input. So if you stop giving continuous input, it will stop doing that. So throttle will stay the same, because that's not a continuous input, it's a state. But if you were turning at the time, you'll stop turning. Unless you're in decoupled, or in whatever rotational thing we allow, then it will stay in whatever state that was.