Guilty Crown Episode 12

I'm currently rewatching it. I stopped watching it at Episode 10 last time, well, because it was getting kind of ridiculous at that time. Too bad Gai died. I didn't like him before but after Shu collected back his memories, I thought, "Oh, he wasn't so bad after all." So, Shu and Gai was the hero of the episode. Gai sacrificed himself in order to save the world or maybe his own intentions too? Before he went down the hole with Mana, he said, "I was able to see you again." And Inori said that Gai said thank you too. 
Another thing I'm wondering about is about Mana. Is she Shu's real sister or is Shu only referring her as 'onee-chan' like an older friend?
So, Gai, Shu and Mana were childhood friends. I didn't get the part when Mana gave Gai the gun and asked him to shoot the star on the Christmas tree. Well, the part which I didn't get was how he got wounded. Is it because Mana did it? 

They're crying because of Gai's death...right?