Good gracious. Am I the only person who thinks the defense attorney just got choked? Like spit down the wrong pipe or something? It happens to me all the time, usually at the worst possible time, and it is mortifying. Both attorneys struck me as just being nervous. It's an extremely high profile case, then add the camera and the scrutiny that will surely follow. I don't know anything about the defense attorneys. Have they ever defended such a high profile case? Murder of a child? Been in hearing with media coverage? I'd be interested to know. However, even if they have, I don't think I could judge anyone for being a little flustered in that situation.
I watched live and I haven't yet had time to re-watch, but having spent a good amount of time in the court room, I didn't see anything that struck me as blatantly unprofessional or discourteous.
Regarding LS, who knows what reason she gave her attorneys for wanting to be off camera, but my bet is that she is VERY uncomfortable with her current appearance. As others have said, the lack of makeup, posing, filters... she doesn't want to be seen. I believe that is as deep as it gets. Nothing to do with shame, remorse, or anything of that nature. I'm fairly convinced she is not capable of those emotions.