Who owned the holy land first between the Muslims and the Crusaders?

Answer 1

The Muslims controlled the Holy Land long before the first Crusaders. The advancing Muslims conquered northern Palestine in 636 and Jerusalem in 638. They controlled the whole of Syria, Palestine and Egypt by 641. Christians and Jews were permitted to remain, subject to payment of a poll tax.
In 1099, the Christians of the First Crusade took Jerusalem and massacred the population, which was predominantly Muslim. They created several small Crusader states, notably the Kingdom of Jerusalem.

In 1187, Saladin recaptured Jerusalem for the Muslims, sparing the Christian population.
The Christians recaptured Acre in 1191, during the Third Crusade.

The Crusaders retained some territory until the thirteenth century, when the Knights Hospitaller left for the island of Rhodes. Although the Muslims now controlled the entire Near East, they permitted Christians and Jews to remain.