OK, I will answer your questions one by one, in the spoiler box, both from the published volumes and scans of those volumes that are not released in English yet.
Spoiler wrote:1. Rin dated Haru, yes? Well, she didn't just one day get tired of him. Akito beat her up badly when she found out about their relationship- that's why she was in the hospital. She broke up with Haru to protect him, and basically figured if she could make him hate her, he'd accept the breakup. She also basically offers herself to Shigure for life if he will help her find a way to help Haru/break the curse.
2. Shigure has NOT slept with Akito yet. He will in a future chapter though. They were just lying around in volume 8. Remember, by volume 9, it has not yet been revealed that Akito is a woman.
3. See #1. Rin isn't trying to get pregnant to get out of the main house; she just wants to help Haru and figures she can by giving the "pervy" Shigure something he would want- sex.
4. Akito IS part of the zodiac, and that's why she can sleep with Shigure without transforming. Remember every time Shigure says, "Go ask God", or something similar. He is referring to Akito, whose role is the god that held the banquet for the animals (the one the cat didn't make it to, etc).
Hope that clears some things up. ^-^ I was just glad we finally met Kureno. There's some good spoilers for him too!