Killua is likely to be completely devastated. He might go into a state of shock at first, not believing that Gon is really gone. Then he could become very angry, either at himself for not being able to protect Gon or at the situation that led to Gon's death.
I don't think so. There haven't been any official announcements or indications that the HxH manga will continue. But you never know, maybe there'll be a surprise in the future.