Can you share the ways the android wear watch can connect to internet while it is not pared with mobile device.( Eg: is it possible to connect via wifi, or data connection).
It cannot and there are no Android Wear devices supporting Wi-Fi, at this time (On March 2015).
Update: Some devices (not all) should see Wi-Fi support incoming according to http://googleblog.blogspot.fr/2015/04/android-wear-wear-what-you-want-get.html