Buğra
Yes. The name is attested with figures such as Satuk Bughra Khan, a Karakhanid ruler associated with early Turkic conversion to Islam.
In Old Turkic, buğra denotes a male camel; it was used metaphorically and as an honorific among Turkic elites.
No. Buğra is a Turkic lexical item and not an Arabic or Persian loan in origin.
Yes; it is a historical Turkic name used by Muslim dynasties and carries no religious prohibition.
Typically as BOO-rah; the letter ğ lengthens the preceding vowel in Turkish phonology.