Past broadcast wont stay forever, for just broadcaster they videos will stay for 14 days but if you have Twitch Prime, Turbo, or are Partnered then they will stay for 60 days. Clips will stay forever no matter what you have. If you have a good day/ flight you can download them and keep them, however I don't know if it will mute the VoD if its muted in the play back.
Also the freezing part try streaming in 720p, not have a bunch of tabs open, and cut down the bitrate a bit that has helped me, I've only frozen twice while steaming.