Re: Lebanon fighting
The partition plan of the British Mandate originally called for a separate state of Palestine and a state of Israel. The maps were drawn for the partition, but the Palestinians refused what was offered. The Israelis declared a state in 1948 and almost immediately the surrounding Arab countries declared war. They lost, but Jordan controlled the West Bank, including Jerusalem, and Gaza was annexed by Egypt.
Another historical note - the partition plan was loosely modeled on the partition of India and Pakistan (because that went SO well) and the Indian government was opposed to the partition of the British Mandate in Palestine.
According to the United nations partition plan, West bank and Gaza would have been a part of the Palestinian state. As you mentioned West bank was controlled by Jordon and Gaza by Egypt until the Six day war.
Until that time there was effort to materialize the West bank and Gaza territories into a Palestinian state until Israel occupied them. For the neighboring Arab states it was never a concern to have a independent Palestinian state but it has always been about getting Israel out of there.
If the surrounding Arab states were to ever succeed in ejecting the Israelis out from there, then the territories they occupy would pretty much become a part of their kingdom and I doubt there would ever be any talk of vacating those territories and creating an independent Palestinian state. And if that ever happened then the guns of Palestinians would be turned on their own Arab brethren from their neighboring states.