When using to the device, the screen becomes unresponsive and frozen, how do I fix this?

Unfortunately, it is hard to determine if the battery or adapter is issue by just eyeballing it. If the adapter is the issue, you can test it by using another adapter, or simply buying a new one. If the battery is the problem, then here is link to a guide that gives instructions on how to replace the battery: Asus Transformer Book T100TAR Troubleshooting