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Hello @GirlSparky01, thanks for joining us, it's great to have you on board! 
At this moment, the Fitbit app only displays your average heart rate for the day, and when you tap on the tile, you can see a graph of your heart rate for the previous days. I think it's a great idea having a live tile with your heart rate data when the tracker is constantly syncing which is why I would like to recommend submitting your idea as a suggested feature, where members of the Community can vote for it and add their comments. This is truly the best way to make your voice heard.
Now, in regards of the sleep that's getting recorded while your tracker is charging, please restart your tracker and monitor it for the next 24 hours. Let me know if this issue is still affecting the trackers functionality.
I hope this can be helpful, don't hesitate to reply in case you need anything else! 
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