It's very annoying how Burnham, brought up in the way of Vulcan logic, is hugely emotional, to the point where she's out of control. Not following orders, having a good cry, striking other officers, verbally attacking others for not following her own moral views, putting the ship and crew at risk, etc. She went and had a bawl on Tyler (after insulting him in the corridors, which he was okay with) because she was afraid she was going to die, after convincing the rest of the crew that the Red Angel had to save her. When she attacked Leland, I just wanted him to smack her back. It was your parents that lied to you Burnham!
The writers obviously don't know how DNA works. First we get told that the Red Angel is definitely Burnham, it is a complete match, it can't be faked, etc, oh, but it's her mum. Who won't have identical DNA to her daughter.
As for Araim's big send off. Like others, I just wanted it to be over. We've had no knowledge or connection with the character apart from a rushed back story last episode, so we really don't care that she's dead, despite all the crew bawling about her like she was a much loved character. She might as well have been just another redshirt.
There is just so much sloppy writing and characterisation. Why is this character doing this stupid thing? Because it's emotional, regardless of whether it's the wrong thing to do. Why are the crew doing that stupid thing? Because it looks cool with the visual effects. Why is Tilly still having to be asked every question twice and being all twittery and silly? Because she's the Wesley.
It's like it's written by people who have never read a good sci-fi book. Who have never seen an episode of Trek. Who have never had to sanity check any crazy script idea that pops into their heads. Who really want their audience to hate their main characters. For god's sake, please aspire to be better than barely average.