Oooops... never saw this question... well... it's been only two years... and somebody on the HârnForum is probably used to wait a while...
OK... regarding your questions:
The system is not just a simple rock-paper-scissors thing... although is has elements of it (and they even suggest to use r-p-s to announce combat strategies... but that doesn't work if the GM has more than one NPC to play...).
Players announce their combat strategies simultaneously (playing cards face down or using dice placed on certain sides works well). They can choose offense, defense, or feint.
Generally speaking, it could be said that:
Offense beats Feint
Feint beats Defense
Defense beats Offense
But there is more to that.
Depending on the combat strategies of two opponents, one of them will get certain bonuses to his skill rolls.
For example, somebody in Defense gets a bonus to his defense roll. If he looses initiative, the bonus is a small one. If he wins initiative, he gets a bigger bonus - or can choose to use only a small bonus and counter-attack.
Generally speaking, by pairing combat strategies, the skill rolls of only one combattant will be modified - and in which way is determined by the success level (loose or win) of an initiative roll.
Initiative is basically a skill roll. As all skills in Gemini, it is based on an attribute (or the average of multiple attributes), modified by his "knowledge level" in a skill group - in this case "combat".
Once the modifiers are determined, both combattants roll a d20 each.
Players have to roll equal or less than their character's chance of success. If they roll successfully, the "effect" of their rolls is calculated. It is the difference between their chance of sucess and their roll (CE - Roll = Effect).
The effects are then compared.
If the defender rolled a higher effect, he was able to block (or dodge) the attack.
If the attacker rolls the higher effect, he hits his opponend.
The difference between both effects is his base damage.
He adds his weapon's damage rating to it, and subtracts the opponent's armour value.
A d20 roll determines where the blow lands (target/strike zone).
He can choose to spent some of his effect to strike a chosen location (the costs depend on the chosen location).
That's it in a nutshell.
P.S.: I have two Gemini rule books, so the following information wasn't interesting for me, but it might be for you: A friend found a PDF of the rule book somewhere in the internet via torrent.