To answer all questions on First Strike:
First, a character with First Strike is considered 'winning' in a mutual destruction scenario. That affects initiative if the battle is in that state (where strengths on both sides exceed the toughness on the other), meaning that the First Strike side gives up initiative when that happens.
Second, continuing on that last part, if the battle ends in mutual destruction, the First Strike side survives.
Third, if there are multiple characters on a side and not all have First Strike, they are only 'winning' in mutual destruction if the character(s) with First Strike can, on their own, overcome the toughness on the other side. Otherwise, it is a 'normal' mutual destruction at that time.
Lastly, if there are first strike abilities on both sides of battle and the battle ends in a mutual destruction state, the characters are discarded as normal for mutual destruction, regardless of first strike. If both sides have characters with the ability, then no character gains the benefit of surviving mutual destruction.