A lot of people here have walked into a trap - Assuming that Jesus was real. Stuff like whether Mary was a Palestinian or a Hebrew is just silly when we don't even know whether Jesus was real or not.
Jesus of Nazareth was an actual historical figure, as documented by a few separate (and non-Christian) contemporary sources. Whether or not you believe in the Gospels' account of his life is a separate issue entirely.
As for the issue of the Old Testament, this is an area where a little bit of understanding goes a long way. Christ himself called out the scribes and Pharisees of his time as utter hypocrites, concerning themselves with the minutiae of Jewish law while ignoring its true spirit and intent. As you said, Christ stated that he came as the "fulfillment" of the Scriptures, not as their "replacement"...but at the same time, he distilled them down to their essence. "You shall love the Lord your God with all your heart, soul, mind, and strength, and your neighbor as yourself"--in Christ's own words, that statement is the Old Testament's commandments in a nutshell.
Besides all of this, the question of whether or not Jewish law even applied to Gentiles who became Christian was one that was addressed in the very early Church. Specifically, the apostles decided that non-Jewish men did not need to be circumcised as a prerequisite for entering the Christian community; the same can be said to hold true for the other aspects of Jewish cultural life. The fact that Christians today don't follow kosher dietary standards is but one example of this.
(Also, does Godwinning a theological discussion count for double points?

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