They didn't know, hence "they were surprised to learn about the Romulans". That's something that should've been covered in any basic perusal of the UFP Wikipedia page. Vance's specific line (to Burnham!) was: "You see, history had forgot this in your time, but the Vulcans and the Romulans were two tribes of the same species that went their separate ways. Your brother started the process of reunifying them." So, Burnham, after spending a year in the 32nd century and then at least three weeks comfortably within Federation Headquarters, never bothered to learn about what happened to the Vulcans.
Apparently not. Given Burnham's tendency to become more obsessive I would say it is consistent. Honestly, it might have been more of a defense mechanism against painful news on top of the struggle with being in a completely new time, and the large amount of changes. It's a lot to take in at once.
Absolutely. But they don't need to ignorize Burnham (my second favorite character!) to achieve this. She should be the one informing the audience analogue of Vulcan's status, just as she had in the first few episodes of the state of galaxy to the Discovery crew. There are many that Burnham could tell about Ni'Var and the Romulans (Tilly, Saru, even Adira who might not even know what a Vulcan is). The only thing that might surprise Burnham is the fate of Spock, and that should be on the supposition that she did not look into Spock's fate (or the fate of any of her family) because it was a sore topic.
I don't think they did. I think she became focus on Earth, on the Federation and on the cause of the Burn. She's obsessive and myopically so.
She remembers to send a signal to ler her brother know she is alright, but does not bother to check the history records, for a whole year, to find out what happened to said brother and any of her family. Nonsense!
It's valid dramatic choice. Plays better with Michael getting all wistful seeing a picture of Nimoy as Spock than going "yeah I know all this. Now let's talk the burn".
huh? what nonsense? the reality is that she's couldn't contact the federation for that info since subspace com was a mess and Sahil outpost probably didn't have 900+ year of historical data as for ni'var i'm pretty sure they're isolationist
Yep, but like I said it works better for the story beats. Like Kirk never once having looked at Spock bio so we can have a dramatic moment in Journey To Babel,
Do organisations list the names of relatives on personnel files? Maybe his next of kin records just said A. Grayson lol