The ottoman empire ruled a vast area, and after its fall, the British and French pretty much had a free reign of the area, and divided it, to which Palestine fell under the British mandate. As far as I understand about the population, they were mixed, the term Arab describes a heterogenous population rather than one single race.

Working through http://www.amazon.com/History-Middle-East-Peter-Mansfield/dp/0786173890 this book. Quite accessible without to many details to bog down a layman

They would have considered themselves Ottoman most likely, then Arab or Muslim. They wouldn't have said they were "Palestinian" in a national sense (perhaps they'd say it as "I live in the region of Palestine" like some would say "I live in the Balkans") until after the fall of the Ottoman Empire in any large number.

For more on the formation of Palestinian identity formation, you can check out my answer here.

As far as before WWI, it was controlled by the Ottoman Empire for roughly 4 centuries, though there were intermittent changes more or less over that time. Still, it was mostly a continuous time of control.