Is it just that phone or have you had this issue with other phones as well? You could try transplanting the charge port from the device you know it works on to the device it is not working on. If that doesn't work, check the connector for the charge port to the logic board for damaged/missing pins. If there isn't any damage and the transplant doesn't work it is most likely IC chip is damaged and would need to be replaced.
Make sure you are using a Samsung official charger that provides enough Amps to the tablets. Tablets draw more power than phones do. It may also have a bad charge port. If the port is loose or damaged it can have an inconsistent connection and will charge and then stop.
The games most likely auto-detected your hardware and set your Graphics level to the highest it thinks you can run them. Try turning your graphics down a level or two. Disabling AA (Anti Aliasing) can also do wonders. If that doesn't work, you may have to many programs running in the background. Try a clean boot. http://www.thewindowsclub.com/what-is-clean-boot-state-in-windows