Why is phone hot when charging/in use and losing charge rapidly?

iPhone 4 model A1332

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About 2 weeks ago, I noticed my phone getting VERY hot in the upper right corner when looking at the screen. Battery takes hours to charge, often never actually reaching 100%. Charge is depleted with very minimal use. The phone is hot when charging and when in use. Cools down some if idle.

I have ensured no apps are running in the background. I purchased two batteries from different sources at the same time to possibly prevent receiving a bad battery and having to await replacement, etc. Also purchased a new charger.

I changed the battery x1 with no significant change. I then deleted email accounts after reading that this provided resolution for some, reset network settings, turned off cellular data, and put in airplane mode.

Still no significant change. I did get a 100% charge ONCE after first battery change but was depleted in less than 2 hours.

I have just installed the second battery. It was at 20% when I turned the phone on. Within 10 minutes it was at 16%. I have placed it on the charger and waiting.

Any idea what is going on? So frustrating! I am at a loss.

Thanks in advice for any insight!