My suspicion on the fight is that it was a test from Captain Lorca and that she specifically wasn’t interferring to see how Burnham handled herself.
I just don’t like petulant Starfleet officers. If he had been a civilian scientist I would have been fine with it. IMO Starfleet is supposed to represent the best of humanity. Stamets isn’t showing the best of humanity (in fact the only one on Discovery who acted remotely like I thought a Starfleet officer should have was Commander Saru).
Why are they screwing around with mycology when they haven’t fixed this basic problem.
I liked Tilly, I was trying to figure out why I liked her and hated Wesley (or last ensign/cadet) and concluded it was because Tilly was portrayed as not yet competent. If Tilly saves the ship based on her super-genius at some point, I’m going to turn on her.