Ping is one of the oldest diagnostic tools. It simply validates connectivity from point A to point B, and in doing so provides additional useful information.
Both children and adults receive harassing or abusive email. Sadly, there’s no easy way to trace it back to a sender who doesn’t want to be found.
It’s typically impossible for the average computer user to determine who’s reading your email, particularly since tracing through a an IP address is virtually impossible with legal assistance. The best option is securing your account from any prying eyes from the start.