Welcome to the forums.
What do your battery usage stats reveal at the end of the day, or before you need to recharge?
Also, can you open the battery graph by tapping it? That will show your signal and awake times history since you last unplugged from the charger.
If you have difficulty interpreting the graphs, post screenshots of them here and we'll try to diagnose.
The update warning is probably malware. Report it to Google:
https://support.google.com/webmasters/answer/93713?hl=en
It may be due to a third-party app that you've installed. Try to find it and uninstall it.
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