I think what you are seeing that video is the AI code running/thinking. It is proably taking a while because it is unclear what to do.
I don't think so, because sometimes I reload and the turn passes quickly.
There is nothing the AI can do except skip a turn, since I am invisible.
Not even one of the most powerful chess computers (Rybka) on the deepest lines takes that long to think, let alone with the powerful processors available today.
Either than it being a bug I don't know.