You need to ask your carrier to move your number from your physical SIM to an eSIM using eSIM Carrier Activation or by scanning a QR code.

Anker PowerWave accessories are a good alternative to Apple MagSafe, but you should keep an eye on overheating. It’s a common problem with most third-party magsafe chargers. iPhone stops charging when it’s too hot.

Battery is probably perfectly fine, but nongenuine iPhone batteries don’t have the health features.

Install CoconutBattery app on a Mac, connect your iPhone with a lightning cable and check the battery info.

Ask the third-party repair shop if there is any chance to replace that battery with a genuine one.