1) Why was he allowed to live in a separate house away from the main Souma house?
2) What is his secret plot? He seems to be planning something but it's hard to figure out in the manga....he seems to be doing some secret manipulations between the other characters (but for what reason?)
1. When a Sohma member becomes of a certain age,he is allowed to move out of the Main House. I'm guessing they can choose to leave or not to. But Shigure's house is still Sohma property.
2. I think(though I'm not for certain) he sees how Tohru's presence in the house has changed Kyou(Kyou tries to calm down whenever he's around her) and Yuki(Yuki didn't have a lot of self-confidence).He's probably mentioned this to Akito as well. I think Shigure and Hotari are hoping that Tohru can break the Sohma curse. They're hoping that she can accept Kyou for who he really is,so that Kyou's own personal problems will be over.
*I'm not sure if everything I said is accurate or not.I'm going by memory for answer 1.*
You should read the mangas(that's what I'm doing).They give more information than the anime :)