Your watch should be able to handle calls via your nearby iPhone (over Bluetooth) regardless of WiFi connectivity. If this doesn’t work something else is wrong, probably in settings as the first place to look. I don’t think this is the Allow Calls on Other Devices setting, on my iPhone that only references my iPad and not the watch. Thinking back I don’t even remember having to setup calls to my AW S3, it just worked automatically once pairing was completed.
WiFi connectivity four the watch is also more out less automatic. The watch should connect to any secured WiFi network where your iPhone has connected - with one major constraint. The watch wants standard WPA-style authentication with a passphrase (like you probably have on your home and office WiFi). The watch doesn’t have a web browser and will not be unable to connect to the wifi I often find in hotels, where you have an open network followed by a web based landing page to allow access. That might be the case with Sprint (carrier?) WiFi
If you find I’m right on both issues above my suggestion is to try telling your phone to ”forget” the current WiFi then reconnect so the password etc is renewed and pushed to the watch. You could also try connecting to a different WiFi when you get home or something... If it still fails maybe there are settings stuck in the watch, so try unpair the watch then re-pair and see if that helps.
Good luck, post back if you still have problems
