What happens when you perform a K-turn, but it ends with your ship being on top of another? The rules say that you move your ship backwards along the movement template, but does the ship still do the 180 turn, or is it facing in it's original direction? If it IS facing in it's original direction, does it still recieve a stress token since it didn't actually make the turn?

As far as I understand the rules you would you would move the ship back alone the measurment stick. you would not do a 180, and you would still get a stress token.

That is the correct interpretation, yes.

Exactly right. The ship still gains a stress because it performed a Red maneuver. Similarly, a Green maneuver that results in a collision would still remove a stress.

However, as the moving ship did not reach the end of the template, they do not get to turn around.

And what about when you end your Koiogran turn on an asteroid instead of a ship? The rules aren't very clear in this instance, and we've played that you still get to turn around on the asteroid. We figure the fact that you are stressed, and can't attack that turn are bad enough.

The asteroid interpretation is still correct. You would complete the move, become stressed, perform no action, and get no attack that turn

That's a good question that I thought I knew the answer to, but cannot find a specific reference to it in any document. Looks like the turn goes through.

Eruletho said:

… and roll for damage

oops, can't forget that! Rolling for damage is probably the best part (as the opponent of the guy hitting the asteroid…)