Basically, is there a way to make the server viewable from outside my network?
MTYou would need to allow or open a port in you router to steer or "forward" the request to the ip address of you Arduino. Also if your using port 80 your ISP most likely blocks requests to port 80 so if you reassign it to port 8080 that should work. You will need to know your ip address assigned to your router you could use whatsmyip google it. Then enter http://youripaddress:8080 on your phone and if all is well it work.Don
The usual way to provide outside access is to use a dynamic IP service like www.no-ip.com or www.dyndns.com and port foward on your router.