With regard to the battery charging issues you mention with your device, there may be Power Management driver updates for your specific system. Follow the link below to look for new driver updates for your specific system. You can also run diagnostics from the Lenovo site as well. As always, be sure to create a restore point on your system before you make any changes. You can do this by just typing "restore point" in the search window within Cortana and follow the link to create a restore point. Here is the link:
http://pcsupport.lenovo.com/us/en/products/laptops-and-netbooks/flex-series/flex-4-1470/80sa/80sa0000us/downloads

Because this is a refurbished model, you will need to check with Best Buy directly about this specific model, as they would be providing the warranty.

It will depend on the software the student will be using. We recommend you check with the specific software publishers for the programs that the student will be using, for their compatibility with Windows 10 Home 64-bit operating system and the minimum/recommended hardware requirements (Is a Graphics card required, the processor speed and the minimum required system RAM and the minimum available hard drive space) to run their program, then compare those requirements to this system's configuration. This information should be available on the software web sites. You might be able to get an idea as to what programs will be used by the student on the school's web site or through the student orientation office at the school.

That depends on the requirements of the game. We recommend you check with the game's software publisher for their compatibility with Windows 10 Home 64-bit operating system and the minimum/recommended hardware requirements (Is a Graphics card required, the processor speed and the minimum required system RAM and the minimum available hard drive space) to run their program, then compare those requirements to this system's configuration. This information should be available at the game's web site.