Rendered Timeline prevents Edits

I'm not sure what you are trying to show in the video. It looks like you have Show Layer Controls hidden in the View Menu. I don't know what the circling selection tool over the bottom left of the comp panel is supposed to do. I cannot tell if you tried to select a layer and reveal any of the animated properties.  

Please be very clear in your description of the problem. If you cannot select a layer and press 'p' to reveal the position property and edit it until you scrub the timeline let us know. If you turn on Show Layer Controls and you cannot see the layer outlines in the comp panel, let us know. 

Impossible to tell you much beyond the usual "Flush the caches and update your graphics driver/ check your GPU settings." Sure, we can see that it goes unresponsive, but since you haven't offer any system information or specific details about the project, we can only guess around. Could even be that one of the pre-comps is the actual culprit.

Mylenium