I think der Leiter is more like leader in a job, it is his job role and der Führer is more like natural leader of others, community or a nation... Not every Leiter is also Führer and vice versa :-) "der Führer" is often linked to Hitler, who assigned this title to himself, so use it carefully
Sometimes a team will have a "leader" (head would be an uncommon term in this case) assigned to a particular project. It just means that this person provides guidance and leadership for that particular project, but doesn't mean this individual is the line manager who gives general orders, makes hiring or salary decisions, etc. In other words, he or she is just a leader, not "the boss". That's only the English explanation, I am not sure that this is the same usage for "Leiter" in German.
The conjugation of "mögen" is irregular.
One of the alternate solutions is odd. The developer likes the head, The head is sometimes used to refer to the toilet (derived from the days of sailing vessels and going to the front of the ship - they had to be careful of the wind direction).