Can someone explain this to me on Dragon Ball Z and GT? (Easy 10 PTS!)?

Ok so I was watching Dragon Ball Z when Trunks kills Freiza with his sword. And I was wondering how Trunks has the sword. I mean he gets the sword from the guy stuck in a music box when Trunks is a kid in the movie Thunder- Fist. But how I mean if everything happens when Trunks says it happens with the androids then the dragon balls are gone because Piccolo dies and they can't wish for the guy in the music box free meaning Trunks can never get the sword from him. So how does Trunks wind up with the sword? Also can someone tell me the ending of Dragon Ball GT I never watched it because I was never into it because Dragon Ball Z I thought was the end. Thanks