About the song... we do know the Federation encompassed 350 alien worlds at its peak from what Vance mentioned.
The song could have originated from a time before the Federation shrunk (aka, before the Burn).
People communicated together throughout the entire Federation, exchanged ideas, resources, technology, science, art, literature (of which music would be included).
Even after the Burn... the music could have stayed with ex Federation members which became part of cultural heritage (a well known 'lullaby' - or at least it may have turned into it after long enough time).. but because it was made so long ago, people cannot remember where it originated from (though I'd imagine that if this was the case, then some record would exist in the Federation database - and ex Federation member worlds would probably STILL have older Federation databases leading to just up until the Burn... or at least, up until when long range subspace sensors/communications stopped working - and when Willa didn't find anything relating to it in the Federation HQ database, THAT could have triggered the notion that its a bit 'unusual').
Also, I didn't like Willa's explanation that 'some things get in the ether'.
Ether is a highly unsientific notion... why would Willa use that nonsense for a description in the 32nd century?
I know she's not a science officer, but come on, some logical reasoning could have led her to the same hypothetical description I just wrote about.
I don't understand why would people hate Vance.
He's from a time when (from his perspective) the Federation got out a messy Temporal War which lasted a good portion of the 30th century which was followed by the Burn.
I didn't agree with him on reassigning the crew, but on conducting debriefings and examining ships/crew's logs, yes (only sensible).
Oh and just because Discovery had Lorca as the bad guy in season 1, it doesn't mean Vance will turn out to be one.
As for Burnham having not much respect for the chain of command... well, she WAS on her own for a full year and she DID let go of Discovery crew during that time, but to be fair, both Saru and Burnham could have mentioned that this is what may make her seem 'abrupt' and 'dis-respective' at times but otherwise she doesn't exactly mean to be... she's merely voicing her opinion (and would it kill Discovery writers to make other characters similarly observant/knowing as Michael is? She's not the only one capable of being the voice of reason or stating the obvious).
To be fair, I didn't like how the writers contradicted themselves twice now with using Burnham.
First it was Culber (or Pollard) who were supposed to accompany Adira to Trill... I'm thinking Culber could have easily done what Burnham did and provide support for Adira.
Same in this episode with the seed ship. Burnham asks for Nhan to accompany them on an away mission because there was a Barzan family on board... and then Culber (again) asks Burnham to talk to Attis (and Nhan, who is apparently of the same species can't make the connection?).
I like MB, but the writers hadn't used her correctly in these instances.
