Well, I did manage to find a few bits and piece. Here's what I can share, at the moment.
According to Tiger Miniatures, this would be the basic structure of the Ottoman Division (at least a division of Anatolian Turks) during the Balkan Wars (1911-1913).
Anyway, again according to Tiger Miniatures, the rough composition of an Ottoman Infantry Division:
3 Brigades of Infantry
A Brigade had 3 battalions of Infantry of 800 men and a Machine Gun Company of 4 Machine guns
A Battalion had 4 companies of 200 men.
A company had 4 platoons of 50 men.
A platoon had 4 sections of 15 men.
Artillery Brigade of 24 guns in 2 Battalion each of 3 Battery's of 4 guns.
Support - Marksman Battalion, 1 squadron of mounted Infantry, a Pioneer Company and a Telegraph company.
...
The "Marksman Battalion" would have been referred to as a Rifle Battalion in the Ottoman Army. They were supposed to be sharpshooting light infantry (so Rifles in the 18th/19th century.) So far as I know they were disbanded after 1913, so probably wouldn't show up in a WW1 era force.
As is the case with most armies of the period, I suspect that the individual makeup of the sections is up to broad interpretation, particularly given that the Turks began to reorganize right before the Balkan Wars along German lines. And, whilst the weapons deployed would probably vary, I strongly suspect that the overall structure would not have changed radically.
One other point of interest that may be useful. I know that the Ottomans had significantly increased the number of Machine Guns by 1916, but according to the information I have in a few scattered notes from various sources, equipment shortages were quite acute during the 1914-1915 phase of the war (they never were completely solved, but matters did improve somewhat in 1916-1917 in terms of automatic weapons). So far as I know, the Ottomans never made widespread use of Light Machine Guns. At any rate, my point here is that the relatively small number of machine guns available to a division would probably have significantly increased by the time of the major campaigns of 1916-1918.
-Alex