Lets get a bit more info on the battery and the charging logic. Install this gem of an app [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] take a snapshot of main window with the MagSafe plugged in and a second one with it disconnected. Post both here for us to see [guide|21499]
I would also recommend you review this Apple T/N to make sure the MagSafe adapter is the correct one as well as the cable & connections are good [https://support.apple.com/en-us/HT203207|Apple Portables: Troubleshooting MagSafe adapters].