I think we have a few problems here. One, it looks like you are trying to record from the live stream. Instead, you should look at the recorded video from the SD card in Playback mode. You can then record any length video clip you like from the card to your device.
The cams dropping connection when the cover is closed is normal at this time (they only expect in-person recording from the live stream). I think they feel if you can’t see the cams, why connect to them? Hopefully they will bring us background audio, where we can lock the screen and continue to hear audio from the cams. The connection would have to stay open then. But in your case you really should capture video from the SD card, which can record the stream 24/7.
I see it does commandeer the audio channel when it loads. Not sure if that is normal or not, never had 2 apps vie for the speaker at the same time. Maybe someone else can chime in on this. In any case I would hope that would get addressed when they bring us background audio.
You can vote for background audio (act like a radio app) here: