Can the new applewatch make or answer phone

In addition to what the other poster has provided, if you are not with the paired iPhone, you would have to have the cellular version of the Watch, and have a cellular plan activated, to be able to make or receive a phone call.

The Wifi version of the Apple Watch can IF the paired iPhone is near and within range

The cellular version of the Apple Watch also can, but does NOT need the paired iPhone nearby to do it. You could be in the middle of a field and as long as you have a strong enough cell signal, your Apple Watch can make a phone call or answer an incoming call.

Neither of the above is new to the iPhone 7. You have been able to do all of this since the Apple Watch has supported cellular.