blinkkite asks:
Hello all,
I was wondering, if a Precise Attack is on a ship I command, can I destroy it with an event destruction card (Worth the Price, Swagger)?
From the Rulebook v3 (page 10, column 2, paragraph 10):
You cannot use game text to remove damage cards unless that text specifically refers to damage cards. For example: Destroy an event. Lose 5 points. This game text cannot remove a damage card that happens to be an event.

garetjax asks:
Can "A few minor difficulties" be destroyed by it's gametext, if the player who commands this event has the Talnot in play and a copy of the event in the discard pile?
And as a second question can i save this event with Miles Repair chief, if it would be destroyed by it's own gametext?
Effects belong to the commander of the card that produced them. When A Few Minor Difficulties destroys itself, it is being destroyed by whoever commands it. Because it is not an opponent destroying it (you are), neither Miles O'Brien nor Talnot can change that.