1] He doesn't really like going out of the house much since that whole episode with Allen on the Ark. Being half-exorcised and then rudely having Joyd wake up all the way just makes him want to kill all those people for what he's lost.
2] Not really fond of randomly killing people he's grown a little recluse and only leaves the wing set up for him alone when ordered to.
3] There are times that he does slip outside, though, when the urges are their weakest so he can continue to look for his precious person. Most of the time it's late at night when he looks or during horrible weather when the streets are more likely to be clear.
4] There's a duck pond in the garden at the mansion he lives at with his brother's family, one that the servants are forbidden to go to. But Tyki's there every day at noon to give the ducks bread that mysteriously disappears from the kitchens.
5] Can spend hours in the library just staring at the books, he won't read them but he likes looking at the different colored bindings and types used for titles. The smell calms him down.