The Stardate Boimler gives places this episode immediately after "Hear All, Trust Nothing", thus this episode would explain the complete lack of Cerritos through most of the following episode "A Mathematically Perfect Redemption" (minus the long time jumps) - they're busy over here.
Pike is a lot less impressed with the badge communicator than Number One is. After all, it's very similar to one he's seen from his own time. Number One missed out on dealing with Section 31 because she was overseeing the repairs to Enterprise for most of that period, so the badge communicator might be new to her.
Given what we would later learn about the Tendi family on Star Trek: Lower Decks, D'vana's grandmother being on the crew of the Orion ship fits. The captain may be a scientist but he was prepared to face many other species and the possibly Starfleet. So he would have a Bad Ass Crew including the "Mistress of The Winter Constellations".
