There is no powers-for-communication thing right now, it's just a consideration that was suggested (though people are free to come up with it on their own as a power for their character it's not a thing everyone has).

The "network" is just the internet so all a character needs is a computer or phone, which can be purchased or created in the characters room (but can't be removed in that case). If Percy actively avoids those things then there's unfortunately no way for him to see internet posts.