You probably have a faulty battery and/or a failing charging circuit and/or corrupted firmware.
1/ Back-up your data. Constant boot looping can lead to data corruption and loss. At least until iOS 10.3 is released as it may not be so prone to corruption from this particular issue.
2/ Restore from DFU. It may help, but I suspect your issue is really the battery, so:
3/ If issue comes back, buy a battery from a reputed seller like iFixit.com (I use their batteries almost exclusively). Bad batteries are the rule, not the exception. Don't be surprised if you get one from Amazon or Ebay or some random seller and the issue worsens or remains the same. Alternatively try using a known good battery to see if those will stop. Once you fit the new battery in, repeat step 2.
4/ Know that you are operating a phone that has set one foot in the grave. Keep your data backed-up. Even if you send it for professional cleaning in an ultrasonic and reflowing all corroded parts, it is still at a big risk of failing partially or entirely.
EDIT: the power button not working may be due to a corroded pin or line or even component down the line. No need to replace it as of yet. Overlay a flat cable over the battery and plug it instead of the old one and test. That's one way.
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