Was there a state called Palestine before? Was there a people called Palestinians before? Who gave the name Palestine?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

1) For sure, there was a state called "Bilad al-Islam" that includes many countries and Palestine was one of them, just as Egypt, Yemen, Najd, Hijaz, Iraq, etc. were countries among that Muslim state
Then, at the collapse of the Islamic Caliphate, non-Muslims divided the Muslim state among themselves, and changed them into small states. After that, they gave Palestine to Jews. This country is still captured; we pray to Allah to free it.
2) As for your question concerning Palestinians, we affirm that Palestinians are the oldest inhabitants of Palestine, and they are still so.
Yaqut al-Hamwi , while commenting on Palestine in his book Mu'jam al-Baldan, said: 'it is the last province of al-Shaam (Syria) from the side of Egypt … 'Asqalan, al-Ramlah, Ghaza, Nablis, Ariha, 'Amman and Yafa are among its well-known cities' . Then, Yaqut mentioned the area of Palestine.
al-Hamwi added: 'it is said that Palestine was named after Palestine Ibn (son) of Sam, Ibn Arm, Ibn Sam, Ibn Noah (peace be upon him)' . al-Zajjaj said: 'it was named after Palestine Ibn Kultham from the son of so and so Ibn Noah, and Hisham Ibn Muhammad said: it was named after Filsheen Ibn Kluskhim Ibn Yafith Ibn Noah' .
Allah knows best.