^The latter is the most likely IMHO. What could just as easily happen is the attempts to draw both states in diplomatically misfires, so neither has any incentive to fight. One wonders how the Allies would have used the troops which IOTL fought in Palestine, Gallipoli, the Caucasus, Suez, and how the Central Powers would have used Boroevic in the Eastern Front.
Indeed. I do think that if the Ottomans did stay out initially, there would be heroic efforts of the parts of all sorts of players to reignite the Balkan Wars, so the Ottomans would have to continue to be in a state of near war either way.
Have you ever heard of any plans to deploy Entente forces to mainland Russia? I would imagine that if the Straits stayed open or something like that, they would have been tempted to investigate the idea