Regarding Har Habayit, there have been a couple of interesting developments recently.

1. An Israeli court recently heard a case of a Muslim woman who had been arrested for disturbing and assualting MK Shuli Muallem on Har Habayit and preventing her unrestricted access. The court convicted this woman for that as well as for preventing access to a Jewish holy site.

The claim made in her defense was that Har Habayit is not in the list of Jewish holy sites and the law defending access to these sites should therefore not apply to Har Habayit.

The judge wrote in his decision that according to Jewish law there is no doubt as to the holiness of Har Habayit and that it is the source of all holiness everywhere else - such as a shul is considered a minor temple and that is why they are always designed facing the direction of Har Habayit..

The Jordanians did not like this court decision and responded that Har Habayit is holy to Muslims and Christians but not to Jews. They pointed to the recent UNESCO decision as proof.
source: Radio Kol Hai

2. MK Avi Dichter (Likud), head of the Foreign and Defense Committee of the Knesset, said in a meeting with Temple Mount activists that the police will be expanding the hours of access to Har Habayit for Jews due to the increased number of visitors wanting to ascend Har Habayit.

Dichter also commented on the Arabs recently calling the entire compound of the Temple Mount by the name Al Aksa which he says is unprecedented when according to Muslim sources only the mosque on the southern end was ever called Al Aksa.
source: Temple Mount News