I would love to be able to livestream (e.g, a sporting event) with real-time remote control of the gimbal. Can this be done, and if so, how?

Unfortunately, the Mimo app does not allow livestreaming without the Do It All handle.  This is a shame. It would be nice if I could livestream via a wired (e.g., USB-C to Lightning, for iPhone) connection to my phone. If it is not built-in to the Mimo app, it would at least be great to have a setting that would allow for a clean interface (e.g., no controls -- similar to a clean HDMI out on a DSLR), so that I could use an alternative app to livestream by sharing the screen. Better yet, it would be great to have a clean screen output, with an invisible touch-screen control for the gimbal, so I can share my screen while still controlling the gimbal via the touchscreen.

Finally, even with the Do It All Handle, it would be nice to be able to somehow control the gimbal while the Pocket is livestreaming via WiFi.  This would allow me to mount the Pocket on the glass at a hockey game, livestream the action, while panning left and right.  

Great idea!

Would love to have this function - live streaming while controlling the gimbal remotely.  If it's supported, every team in my daughter's soccer club would sure want to get one.

You used to be able to do this with the Osmo Plus. I worked with music festivals where I would mount the camera infront of the stage powering the camera with an external battery. I would control the gimbal from my phone wirelessly while sitting at the side of the stage. The sucky thing was the app used my phone mic instead of the OSMO Plus. So no one could talk around me while streaming.