Spacebar seems random. Using it I've won battles where the opponent had +6 points to my +3. So it definitely doesn't go to the one with the most charisma.
No, but it might go more often to the guy with the most charisma.
If the program rolls d20 internally, +3 charisma difference means a 65% chance to win instead of a 50% chance. In effect 2 out of 3 decisions are won by the more charismatic. With 5 points charisma difference that would be 3 out of 4. Not that random anymore.