India is where I always placed Calormen's origins. There is even a god that is similar in attributes to Tash. I will admit that, yes, there are elements of Turkey, maybe, in Calormen culture. I see more Indian than Turkish though, especially if you throw in the the description of the inhabitants. Turkish people tend toward the olive-skinned complexion of the Mediterranean region. Indian people are have darker complexions. So much so that some British authors called them blacks (Frances Hodgson Burnett in Secret Garden would be one such author). If you read the description of India that Frances Hodgson Burnett gives one would see why my mind automatically goes to India.
I cannot see any relationship between God's Holy City and Tashbaan, the only thing might be the hill that leads up to the temple, but that is it. Jerusalem is not the only city where the Temple is at the highest point. Like someone else said, more parallels can be drawn between Narnia and Jerusalem. As to the conquering/re-conquering of Calormen, the implication of Rabadash the Ridiculous is that Calormen, except during the reign of that Rabadash was an ever-expanding tyrannical empire; the big fish that preyed of the little fish in the pond. HHB was pretty specific that Calormen was the dominant power in the Narnian world and that the Tisroc had the numbers when it came to a land battle. Lewis also states that Rabadash was far more concerned about interior threats to his power than exterior, he was peaceful because he did not want his generals to get the glory for winning battles because, I quote, "for that is the way Tisrocs get overthrown." Indeed, other books that deal with Calormenes and Calormen make it clear that Calormen is the most powerful, the Lone Islanders use the Crescent and the Minim. Calormen was NOT the constantly conquered Jerusalem, rather it was more like the constantly expanding Rome.