Same WIFI network: on this https://discussions.apple.com/message/28204946#28204946, the Watch can connect to the iPhone through WIFI, and not only Bluetooth. But not everything will function normally, just message and ping …
OS1 without iPhone :On http://www.idownloadblog.com/2015/04/27/apple-watch-without-paired-iphone/, it shows that some Apple Watch apps like Activity, Tracking and Apple Pay still function without iPhone.
No. From this article http://appleinsider.com/articles/15/06/14/apple-is-making-the-watch-better-by-making-it-even-more-realtime, if you have no iPhone connected (through Bluetooth or same WIFI), the Watch would not receive notification.
“Your notifications will go to your iPhone or your Apple Watch, depending on the device that you’re using.
If your iPhone is unlocked, you’ll get notifications on your iPhone, instead of your Apple Watch.
If your iPhone is locked or asleep, and your Apple Watch is unlocked and on your wrist, you’ll get notifications on your Apple Watch.” – Quoted” – Quoted
So, the iPhone has priority (over the Watch) to receive notification , if the iPhone is locked or asleep and you watch is not locked (with a passcode) -> you get the notification on Watch.
WIFI Firewall Issue
“For APNs traffic to get past your firewall, you’ll need to open these ports:
- TCP port 5223 (used by devices to communicate to the APNs servers)
- TCP port 2195 (used to send notifications to the APNs)
- TCP port 2196 (used by the APNs feedback service)
- TCP Port 443 (used as a fallback on Wi-fi only, when devices are unable to communicate to APNs on port 5223) ” – Quoted