ENDO
Go ahead and use the pump, it’s designed for water!
My well pump is run on 220 and no GFI protection and has a plastic pipe to the house.
I would wire it after the GFI outlet and put in a dedicated 1 amp fuse.
You can get a fuse holder from an electronic supply house. It has a screw cap with the fuse under it. As to grounding the sink and faucet! Why? If your house has plastic pluming, they don’t ground the sink or faucet!
Chuck