If you are using a recognised charger and not some knock-off, then using the phone whilst it is being charged will not damage either the phone or the battery.
Some links I found when I Googled, "Can I use my phone whilst charging the battery?"
http://mashable.com/2014/06/18/phone-charging-myths/ and
http://www.techrepublic.com/blog/10-things/10-common-misconceptions-about-mobile-device-batteries/
I hope that helps.
Mark
Specifically, using both a music app like Pandora or other plus the phone's light application, all through the night. Will doing this, while keeping it on charge, on a nightly basis risk damage to the battery?

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