Point 1: Absolutely correct, as bitpicker has noted. In fact, Jesus Christ is praised in the highest terms in all Islamic texts. And the first time I read about Saint Mary in Quran, I was almost moved to tears. True, that was long ago...
Point 2: I don't know about the Christian sources, but according to the Islamic sources, Hagar was left in the desert by Abraham (not Jacob, who was Abraham's grandson, I think). Mohammad was a descendant of Ismael, Hagar's son.