But on a slightly more serious note, can someone shed some light on this for me, because I don't know nearly enough about their history: Are the Palestinians related in some way to the Philistines of Biblical times?
NO.
Nah. The Philistines were part of the 'Sea People' who probably originally came from Greece. The Israeli area was given the name Palestine, after the Philistines, by the Romans when they conquered the land, even though the Philistines only lives along the southern-most coastal area. I guess they thought more highly of the Philistines than the Jews.
Today's Palestinians, then, are just Arabs who moved into the land.