Emergency Calls without phone

Everything deggie said, AND you have enabled WiFi calling on your iPhone -> Settings -> Cellular -> Wi-Fi Calling -> enabled, AND you have enabled WiFi calling in the iPhone -> Watch app -> Phone -> Wi-Fi Calling -> enabled, AND you have configured your iPhone WiFi calling location correctly so that the correct emergency services is called, and they show up at the right address.

That is a lot of ANDs you have to line up to insure you can make emergency calls.

It would be better to assume you need to keep your iPhone nearby. That can be within Bluetooth range, or on the same WiFi network so the iPhone and Apple Watch can talk to each other.

If you are connected to a WiFi network that supports WiFi calling yes, if you are just out and about, no.

IF you are connected to the WiFi network, IF the network supports WiFi Calling and IF your cell service provider supports WiFi Calling.