The cable company system should be completely separate from your OTA system. It sounds as if it is, but I want to emphasize that you want to avoid connecting an antenna to a cable network connection, even if it's just providing internet access. You don't want to interfere with aircraft navigation and communication frequencies or other licensed radio services.
One ground connection will protect all of the OTA coax distribution system. I would only ground one splitter... the one closest to a convenient ground connection. I would use a piece of #10 copper wire (bare or insulated, your choice).
If the well is dry and you don't see rain on the horizon, you'll need to dig the hole deeper.