An explanation for Han and Chewy not being in possession of the Falcon is that they have simply outgrown her. If you think about it, Han especially was both leader and victor of the most pivotal battle to date. This would probably have propelled him into a position of high authority. The Falcon is also kind of a bachelor smuggler's ship. If he married and had a child/children with Leia, he would have had to give up that life.
I've read that the person handing Leigha the light saber is Lupita Nyong'o's character, who is reported to be a short, somewhat CGI alien