Regarding Koran vs Qur’an, I much prefer Qur’an as a more accurate transliteration, although eliminating the apostrophe is fine too. Regarding Muhammad, I prefer this spelling when referring to the Profit. One can spell one’s own name however one likes.
And, I applaud Fox News for using Usama instead of Osama. Since there is no Arabic letter analogous to the English o, I see no validity for its use in transliterating Arabic to English.