What other religions did Judaism play a role in the development of?

Answer 1

Christianity and Islam.

The Hebrew Bible has been accepted by Christians among their scriptures. Islam too, was heavily influenced by Judaism and its texts, both directly and indirectly.

Very many concepts and quotes in the Qur'an (the book of Islam) are taken verbatim from the Torah, the Hebrew prophets, and later Jewish teachings. The Talmud was already recorded in writing by no later than 500 CE*, before the time of Muhammad, making it a simple matter to quote from it too.

*(Footnote: as stated in the Encyclopedia Britannica, under "Talmud and Midrash.")
Arthur Jeffery writes in "The Foreign Vocabulary of the Quran", in page 1 of the introduction: "One of the distinct impressions gleaned from a first perusal of the Quran, is that of the amount of material which is borrowed from the religions that were active in Arabia at the time when the Quran was in process of formation. It is plain that Muhammad drew his inspiration not from the religious life and experiences of his own land and his own people, but from the great monotheistic religions which were pressing down into Arabia in his day."
Charles Torrey in "The Jewish Foundation of Islam", writes on page 43: "It was at home, not abroad, that the Muhammad received the Biblical and Haggadic narratives which occupy so large a part of the Koran."