The Ottomans can constitute a large enough force to make the British expend efforts to protect Suez, so in late 1914/early 1915 there needs to be something there, and even absent the Western Front it will take time to build enough force to attack the Ottomans in Palestine. remember whatever of the BEF was evacuated from France there have been personnel losses and equipment losses from moderate to severe - that takes time to rebuild. No Marine Nationale means the RN has to protect the Med on its own, while keeping the Home Fleet as a shield against the HSF and dealing with the early U-Boat threat. Italy is at best neutral, so the AH forces have free access to the Med, if Italy has joined in that makes life more difficult for the RN.
The reality is that even if Gallipoli goes off on schedule and is successful, it will be a slog before the British arrive at Istanbul. OK late summer 1915 the Ottomans give up - does that really help Russia? Not that much, and even under the most optimistic, maybe even ASB, results bu the time the UK could knock the Ottoman Empire out of the war the Russians are either out or close to it. Even a relatively free supply line to Russia through the Med/straits/Black Sea is not going to solve the Russian problems. All of this assumes the UK is willing to make the sort of sacrifices in blood and treasure needed to get to this point, still far away from Germany defeated.
Had Germany not invaded Belgium, getting support for Britain entering the war would have been difficult at best. If Germany agrees to leave Belgium, maybe even use some of the money they get from France to fix the damage, why should Britain fight. I also wonder how eager Canada, Australia, New Zealand, South Africa will be to send forces in to a fight where France is out and at best they are fighting for Russia.
I disagree about how many divisions Germany needs for French occupation. They only need to have a significant presence in territories to be annexed or occupied (like the Rhineland) for a longer term. For the rest of France once they supervise demobilization, collect guns etc only a relatively small number of monitors were needed - look at 1870/71 and once France gave up, Germany did not have armies all over France. The only place you'll see Germans other than as noted is a few channel ports - to prevent the British from waltzing over and to prvide support for the HSF.