6.5 says "The friendly senior heir in a battle at the instant of fire has the option to Charge." What exactly is meant by "at the instant of fire"? Is this a reference to the moment when that particular heir has initiative and would otherwise make its regular roll to fire?
Yes. Whenever it is the senior heir's turn to fire, he may instead charge. The 'at the instant of fire' only clarifies what happens if seniority changes because of reserves, retreats, or elimination of an heir.
If the heir charges before the battle actually begins is he allowed to fire in the first turn when he has the initiative?
You cannot charge 'before the battle begins'. You charge instead of making a regular attack during the battle.
If both player 1 and player 2 want to charge with their heirs who goes first? Player 1 or the one with more senior heir?
Initiative is determined as always. Defender before attacker, A before B before C. You do not compare seniority of heirs between the two sides.