The only information I've been able to find is that the US sent some crated Hawk 75 fighters to Persia, which were captured by the British and used as Mohawk IVs.
Yes. The date at which each country's air-force was established was largely dependent on when they gained independence. Iraq prior to its independence in 1932 was actually under the military authority of the British RAF. The RAF helped create the Iraqi air force in 1931.
Egypt also had an airforce. As did the Israelis at the time of their independence in 1948. The '48 war did involve air combat, though not to the extent that it would come to dominate the '67 and '73 conflicts.
The Turkish air force was arguably founded by the Ottomans and were to my understanding the largest air force in the region at the time.