Q: Does shared photo stream require Wifi or does is work with 3G?

Originally everything that had to do with photostream required wifi. It still does according to the rules and articles even for regular photosthream. What changed is that LTE provided faster and more reliable connection then some people's wifi. Hence amount of people on community forums that scream that their data usage increased. Some of them just have problems to configure their routers to accommodate "non drop" connections. So in order to upload any photostream to icloud server, constant flow of datastream with constant "handshake authentication" (lets call it that) required. If your cellular can provide that, you don't need a wifi. Problem is your connection(unlike wifi) is dependant on your location, so there is no singular answer to the question "if cell network is ok". For the same reason your "work" wifi may not be OK, since every smart work place blocks authentication ports for reason. BTW all of that is obviously JMHO.