Is it possible to upgrade the S7 Slim from the shipped Android OS of version 2.2 (Froyo) to 5.0 (Lollipop)?

It might be because of a bad battery. Since it doesn't charge via the adapter option, try connecting the tablet to a computer using a mini-USB cable. If it again doesn't charge, that implies the battery is faulty and needs to be replaced. Use this guide to replace the battery.