cdn.esoui.com doesnt serve a webpage, it serves downloads. so you would need to go to
http://cdn.esoui.com/downloads/getfile.php?id=128. We currently use Akamia as our CDN provider so it chooses a server that is closest to your location and sends the requested file.
Minion uses the standard port 80 and secure ssl 443. Most people should have these open.
Right now if Minion can't connect to the internet its going to cause it to crash/hang. In a future patch we will have a message that displays that Minion can not connect to the internet so it wont cause the client to crash/hang.