As a long time resident of Pisgat Ze'ev, I can tell you that yes, Israeli and Palestinian (East Jerusalem residency holders) Arabs can and do live in Pisgat Ze'ev. In recent years, many residents of places like Shuafat and other areas now past the security fence have relocated to Pisgat Ze'ev because they do not want to lose their rights to Israeli/Jerusalem residency if those areas on the other side of the fence are turned over to the PA. Also, a significant number of Christian East Jerusalem Arabs have chosen to buy apartments in Pisgat Zeev. Our neighbors are a lovely Christian Palestinian family who moved to Pisgat Ze'ev because apartments are cheaper here than in the nearby Arab enclave of Beit Haninia. For the record, there are absolutely no laws in Israel restricting Arabs from moving into predominantly Jewish neighborhoods. Despite what you may hear, Israel actually has very tough anti-discrimination laws.
Italian FM arrives in Iran to promote economic, political ties (Reuters)
from the article: Council approves construction of 32 new homes in East Jerusalem