The interface with Periscope is an industry camera. Any 360 camera will work. Though, I think the THETA V has advantages with live streaming 4K video. Please check the specifications and user feedback for each camera you look at. You can see on this forum that live streaming with the THETA V is popular. Note that the THETA S can only live stream at 2K. I highly recommend the THETA V over the THETA S for live streaming.
Each person viewing the live stream can see a different view.
The “viewer” angle changes, not the camera. The camera is in a tripod and does not need to move. If you move the tripod, the viewer can still rotate their head or use a mouse to change the view.
See this article: