Christianity views the acts and life of Yeshua of Nazareth as the fulfillment of the promises and prophecies made to the Chosen People in the Old Testament. The writings attributed to Matthew, Mark, Luke, and John chronicle that fulfillment.

If you do not accept Yeshua as the Messiah, as the Chosen One, then the NT is irrelevant to you. You still await the Messiah. On the other hand, if you accept Yeshua as the fulfillment of the OT promises and prophecies, then why still revere the now-irrelevant (to you) Old Testament?

I was taught that the early Christian Church moved their day of worship from Saturday to Sunday to distance themselves even more from the Jewish faith.

For a discussion of the date of easter, see here.

As for the physical existence of Yeshua, I find it hard to reconcile the 18th and 19th Century views of Paine and Ingersoll -- correct in their time -- to the 20th Century discoveries at Nag Hamadi, the Gospel of Thomas, the Gospel of Mary, and others such writings. I suppose that, in the end, it's a matter of what you want to believe and what you're comfortable with.