Whatever I have read:
https://www.amazon.com/Berlin-Baghdad-Express-Ottoman-Empire-Germanys/dp/0674064321
(something downloadable)
https://ora.ox.ac.uk/objects/uuid:55dd46e5-2eef-46f6-be8b-ca7bb177a518/datastreams/ATTACHMENT1
Shows:
a) Different German/Turkish viewpoints on Persia strategy
b) Difficulty in influencing the area due to distance and communication issues.
c) Persian army forces are smallish and dispersed around country
So: on your questions
1) No - maybe you can cause the British some distractions, delay the capture of Baghdad if the British are more distracted by events in Persia, however one could argue that if the Germans/Turks would have completely ignored Persia during WW1, focused on building a defensive position after the fall of Kut they might have been better off.
2) Maybe nothing significant gained, Having a strong Ottoman empire next door would be dangerous to Persia, worse than OTL British or Russians, OTL (our time line) the war sort of weakened everybody around so was good for Persia.
3) Might have become a full out British protectorate, more likely a government favorable to British would be installed. British would expect some compensation for losses.
Ok on #1, a stretch Central Powers victory is caused by:
The revolt in the "stan" regions of Russian central Asia
https://en.wikipedia.org/wiki/Basmachi_movement
This revolt in the "stan" regions of Russian central Asia. Perhaps if the Germans and Turks had greater visibility in the Northern Iran area, they could assist with a handful of officers and some machine guns via Persia and turn this into something big. Perhaps as a POD the Turks don't launch their 1914-1915 Winter offensive in Armenia and so are in a better position to influence event in Northern Persia in 1915 and assist a friendly Persian government and thus are able to assist this rebellion.
The Kerensky government faced with this, amongst their other problems, negotiate a separate peace with Germany. Germany launches a larger offensive into Italy in late 1917 knocking her out of the war.
Germany lunches a 1918 offensive in greater strength in France capturing Amiens and forcing a favorable compromise peace.