Frequently "Network Error"

Nope, could be a overheating issue. I would probably recommend not charging your phone while playing since it could overheat your phone.

This happens to me when I am in areas with bad reception. Try restarting app and moving to another area?

I believe use better phone(high speed) will help.

Yeah. It's been happening to me at 2 places I frequent. I can't catch, spin, it gym there. I just get network errors. A couple times I got in a gym battle but it would kick me out and then I'd time out in the background