Until the 1960s, Palestinian was used alone to mean Jew, except when it additionally specified Palestinian Arab. I have seen Jewish ID cards from before the State of Israel that identify the holder as Palestinian. There might have been paper money issued by Jews with Palestine on it, IIRC.
That is right. Issued by the British Protectorate. Britain was appointed as the Protectors of Palestine. Palestinian was used to mean anyone living in the Protectorate, until the War of Independence in 1948, when Israel was declared a Jewish Nation. Arabs are presently called Palestinians because they never accepted Israeli Independence.