These ships are touching each other and parallel. Next turn each ship will perform K-turn at the same speed. Q: Will one of these ships overlap other?

No they will not overlap.

If ships overlap they end up touching. Touching does not constitute overlapping.

If ships are touching but did not overlap there is neither an action loss nor a shooting limitation.

Edit:

Fighter and Bomber will not perform K-turns at the same speed. But that is a different story.

No they will not overlap.

If ships overlap they end up touching. Touching does not constitute overlapping.

If ships are touching but did not overlap there is neither an action loss nor a shooting limitation.

Edit:

Fighter and Bomber will not perform K-turns at the same speed. But that is a different story.

There were two TIE Fighters in that game Thank you for answer