Here is what has been happening in East Jerusalem in regards to rights.
Israeli courts has upheld a 63 year old controversial absentee landowner law that allows for the confiscation of Arab-owned properties in East Jerusalem. The courts specified it was legal but should be used rarely. The "rarely" part seems to be abused. According
to this article, "the court said the state may confiscate East Jerusalem property held by West Bank residents".
Jewish settlers, such as the rightwing Elad Corporation have been moving into the traditionally Arab sectors of Jerusalem benefiting from these absentee confiscations as well as buying up property under false pretenses.
The absentee landowner laws forced Palestinians to sell because they were not allowed to return.
Other means of purchasing and "occupying" property are also questionable, for example:
Sudden apartment takeovers in east Jerusalem spark anger
Jewish real estate deals in the contentious Silwan area have long been murky. Purchases often go through intermediaries, which those involved says protects the Arab sellers from being attacked by their neighbors. In some cases, Arabs who say they are the rightful homeowners take Elad to court, arguing the properties were sold by imposters posing as homeowners.
Residents move in at night while Arab neighbors are asleep. The Israeli government bankrolls armed security guards to protect the Jewish residences, many of which are equipped with blooming geranium bushes, Israeli flags and security cameras.
Elad long has attracted controversy because of its nationalistic agenda. But Elad says the area is central to Jewish heritage, and investment in the area has benefited Arab and Jewish residents alike.
“We would like to see a majority of Jews living in this area,” Spielman said. “Having said that, we respect our Arab neighbors.”
About 500 Jews live in the area, and the newly purchased homes will allow for 200 more, Spielman said.
Until residents move in, the properties are occupied by police officers, private security guards, and young volunteers packing pistols. An ad on a Facebook page for religious Jewish army veterans offered 500 shekels ($140) a day to anyone willing to sit in the properties.
On Thursday, Israeli police officers disappeared down a narrow concrete alleyway, bringing a box of supplies deep into the Arab neighborhood to a second-floor apartment. The Israelis peered out from windows they enveloped in wire mesh, and would not open the door to visitors.
In a narrow alleyway below, an exasperated Palestinian woman, 23-year-old Bushra Mohammed Adel Khayyatt, said her laptop and jewelry were stuck inside the apartment, and that her knocks on the door and pleas to get her belongings back have gone unanswered. She insisted her family had not sold the apartment.
A group of young Palestinian residents gathered and screamed at her, accusing her family of selling their home to the new residents.
“Are you crazy?” she retorted. “How would my father sell to Jews?”
What often happens is the Arabs are unwilling to sell to Jews but intermediaries claiming they will not do that do just that. They are often employee's of corporations like Elad so it is a very deceptive practice. On the othe side of course - Arabs who sell to Jews face retribution from family and neighbors. And perception matters. They can say Arabs are allowed to live anywhere in Jerusalem but that is not the case in reality. Most "settlements" are Jewish only, even though the laws state that they can not have rules that discriminate ethnically they do.
Are there any new Palestinian settlements in West Jerusalem?
Is there any reason NOT to believe that increasing the number of Jews living in East Jerusalem and decreasing (through lack of residency permits, dishonest selling practices) - is not a means of gaining ethnic control over East Jerusalem?
It's a complex problem, and to add to the mess is housing costs in Jerusalem, which are so high that the Palestinians, who are NOT subsidized by outside groups - simply can not afford to live there.