What irritates me greatly is when historians refer to the Muslim scientists of the Islamic Golden Age as "Arabs", when most of them were not Arabs at all. It's such a simpleminded and sweeping generalisation that clearly shows the thoroughness of the so-called orientalists.
I agree with you about the second point. I guess it's due to the fact that they wrote in Arabic and many of the people they actually belonged to no longer exist (for example al-Khwārizm was from a Persian family but born in what is today Uzbekistan - I actually visited his hometown :)
To me it's strange to ascribe such areas of study to the religion. What does Islam really have to do with optics besides Ibn Al-Haytham being a Muslim? No one ever ascribes enlightenment science as 'Christian science'.
Hence the 'weaker' nation feels deprived of its history when its proudest moments are appropriated away.
We don't call the Spanish conquest of the Americas a Christian one even though they were Christians who ultimately converted everybody to Christianity.