Is Christianity based on older myths?

[Nope]

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Furthermore, during the Greco-Roman period of Jewish history, Jews actually engaged in actively promoting conversion to Judaism. In a well-known story in the Talmud, a Roman asked Rabbi Hillel to “teach him all the Torah while he stands on one foot.” Hillel responded, “What you do not like done to you, do not do to your fellow; this is all the Torah. Now go and study it.” This Roman embraced that principle and converted to Judaism.
This story is by no means an “exception.” In fact, thousands of non-Jews living in the Roman world, and everywhere in Asia and Africa, embraced Judaism. While Judaism does not seek out people to convert, it is, and always has been, open to welcoming anyone who sincerely embraces Jewish life.

http://bethshalomnc.org/conversion/
http://www.israelnationalnews.com/Articl...NPJW53F_iU

Judaism was the most active proselytizing religion from the Maccabean period (though the Hasmoneans sinned by forcibly converting the Idumeans) through to the time when Rome finally embraced Christianity. Then the Church fathers, using the temporal power of Rome, banned Jewish missionary work upon pain of death. Thus the current tradition of discouraging such proselytizing emerged and has lasted for over a thousand years.

Before the rise of modern Christianity, some Jews tried to win converts. In order to gain converts they would have had to interact with Romans and would have gained some knowledge of their beliefs. It isn't hard to believe that the stories from both culture would have influenced each other.