I have another post about it and iPhone v Android, but so you can get an answer here:
Do you have it connected to any network?
Not sure what you mean. I have an AT&T Urbane, it is on ATT LTE. When connected to iPhone there is no other connection such as WiFi.
Can you answer calls or emails or just receive notifications?
Just notifications with iPhone.
Can you make calls from it?
Yes, the watch all by itself is a phone. You can dial from the watch and make (and receive) calls. It has its own number. However, what you have is the watch speaker and microphone for audio. In a totally quiet situation, this is sufficient. Any background noise whatsoever - like when driving - and you will have a hard time hearing it. The other end can hear you fine, regardless. When connected to an iPhone, you can't use a bluetooth earpiece with it. So, yes, it works as a phone, but while connected to an iPhone, that has limited utility.
Also, with an iPhone 6 you can do number pairing so that if your phone rings your watch rings. So you could, theoretically, answer a call that comes into your iPhone, but the limitations on audio above apply.
What running apps can you use on stand alone mode, not connected to the phone via BT?
The time. And to an extent Google Health.