What right do the Palestinians have building their mosque on the holy site of Solomon's Temple?
You make a good point here, but what evidence is there that there was ever a temple there? I have searched and have come up empty. Have you anything to verify the temple's location? Thanks.
Is there evidence the Muslim Pegasus ever flew over Jerusalem? Exact location maybe...
No, only Muslims believe in it.
However, all 3 Abrahamic religions, including Islam (and Jerusalem Arab Mufti) recognize Jewish connection to the Mount as location of both Temples.
Again, Christians and Muslims each believe their own things and argue...one thing they DON'T argue is the location of the Temples in Jerusalem on Mount Moriah.
This denial on part of the Muslims is only recent - and mainly politically driven.