Who refurbishes the phone? Is the battery replaced when they do so?
A 3rd party refurbishes the phone. The battery is checked and replaced if needed.
Will this phone work on the Sprint network?
According to the features: In the US, Pixel is compatible with GSM-based networks AT&T and T-Mobile and CDMA-based Verizon.
Which is wrong/misinformed, since in the United States there are two models of the Pixel.
There is the Verizon model which can be used on ALL carriers, but cannot be rooted.
And then there is the rootable version which also works on all carriers.