Some notations on the Starship Combat Cheat Sheet:
* Initiative is rolled only once, at the beginning of combat. (THB, pg 150, last paragraph, right column: "These initiative check results determine in what order vessels will act during each round of the encounter." Also, it's consistent with how initiative is handled in the D20 System.)
* Point Defense Sandcasters may be fired against incoming laser fire as well, according to the ruleset. (THB, pg 162, first sentence of Point Defense Sandcasters.) I agree with you that a sandcaster should not be able to react to an incoming laser moving at the speed of light, but I'm assuming that this rule represents sensors detecting the tell-tale signs of powering up immediately before firing, or something like that, as a justification for the rule being present.
* Anti-Missile is not required for laser point defense against incoming missiles (Gunners can do that), but it's definitely a good idea.
* By the rules, Overpowering Weapons and the use of the Double Fire program are not mutually exclusive. Personally, I would have rather seen Double Fire written up in a manner similar to Rapid Shot for vehicles, with two shots but both at a -2 attack penalty, but that's the D20 System nut in me. If you are looking for a home-grown solution to that one, I'd suggest making the Overpowering Weapon roll for each attack, increasing the -1 penalty per round to -1 penalty per shot. This is, of course, a House Rule, and subject to your own tastes, as you see fit.
Hope this helps,
Flynn