Charles Xavier II is the son of Professor X and Mystique from roughly 25 years in the future. He was given up for adoption immediately after his birth, and Mystique checked into the hospital as "Ms. MacTaggert". His adopted mother called him Charles, but his legal surname is unknown.
Xavier II was initially born in the Earth-616 timeline. Professor X and Mystique engaged in a secret marriage from which Xavier II was conceived and then born shortly after Professor X's death in AvX. Charles I's marriage to Mystique was acknowledged in his will in Uncanny X-Men (3rd series) #24 but, after Eva Bell altered the timeline, the marriage was not referenced in the new will heard in #31. One could extrapolate that Xavier and Mystique's relationship no longer occurred at all, and Xavier II therefore no longer has a 616-counterpart.
Xavier II was paralyzed by future Colossus's Soulsword, but used time travel to undo those events and create a divergent version of himself who was never attacked.
Magneto confronted the Brotherhood in the timestream in X-Men: Blue #20, implying they did not survive the encounter.