Uhura didn't join the Enterprise until Kirk did, and the people working on Strange New Worlds know and respect that fact and won't contradict it.
We don't know that, the only line to imply it is Mr. Adventure's line about a 20 year career, and we know that's inaccurate because she was in Starfleet before 2265.
because Spock is the only TOS character who served under both Pike and Kirk
Gary Mitchell