
It wasn't a country, but the region was commonly referred to as Palestine for centuries until 1948. The countries nearby weren't really countries until the ottoman empire was carved up.
No... The name comes from the Romans, and was an intentional slur against the Jews after a revolt, 'reverting' the name back to the Roman rendition of 'Philistine' and 'Philistia'. Antisemitism then as now.
The name fell out of use rather quickly since it was a political gesture, and is nearly absent until after the Ottoman Empire... Coincident with the rise of Zionism and the establishment of Israel.
Historically, the land is named Canaan or Israel. 'Philistia' refers specifically to the area known as Gaza today, and not the region. It was a confederation of 5 cities: Ashdoid, Ashkelon, Gath, Gaza, and Ekron. Philistines were invaders that expanded by war across southern Canaan as far inland as Sodom and the cities of the Plain, but were stopped in their expansion, and beat back into the area of those 5 cities.
Ironic ain't it? And here you are, literally rooting for the Philistines. Invaders now, just like then.