I have a question regarding the Overlapping In-line Ships rule.

Overlapping In-line Ships explained in FAQ:

Scenario

First round

I have 2 Tie Fighters on in front other one behind. Front Tie Fighter moves with a 2 straight. Then the Tie behind him moves with a 3 straight. As a result they are overlapped and considered touching, no action for him.

Next round

The front Tie moves with a 2 straight. Then the other Tie fighter also moves with a 2 straight. What I read from the Overlapping In-line Ships rule he is not considered touching so he now can take his action.

Am I correct?

Yes.

And what if the both do a Turn with speed 1 or 2?

Assuming you don't run afoul of spatial drift and overlap with the second one, they aren't touching after they both perform a turn, provided they're of the same speed.

Assuming you don't run afoul of spatial drift and overlap with the second one, they aren't touching after they both perform a turn, provided they're of the same speed.

Yes I ment with the same speed so first one with 1 turn and second also.

With a turn you should be able to run a line diagonally across both starting and ending positions. With two inline ships there should be room to make that maneuver. NOW if two ships are side by side and try the same thing they will NOT make the turn; if nothing else the nubs make the base a bit longer than they are wide which means they will not fit together so well after making the turn.

I have had a ship end up touching an opposing ship, but it did not overlap at all. Does this ship still lose it's action?

No. If you do not overlap you are not considered Touching.

I have had a ship end up touching an opposing ship, but it did not overlap at all. Does this ship still lose it's action?

No. The only way two ships can be "touching" is if there is an overlap or there was an overlap and the ship doesn't move. If you can complete a maneuver being physically adjacent to another ship will not prevent you from skipping your Perform Action step or attacking said ship if it is in your firing arc.

While you could barrel roll a ship into a physically adjacent position you can no roll it into a touching position that would prevent attacks between the two ships.