That's some lore I'm just not familiar with... 
In the first two episodes she appeared in, the Corbomite Maneuver and the Man Trap, back when she was a day player rather than regular cast (ditto with Takei at the time), Nichols wore command yellow, rather than Operations red:

The producers decided she looked better in red, and so switched her to a red uniform after that.
Her being fourth in command, I don’t know: I don’t know who has more time in grade between Sulu and Uhura off the top of my head.
Edit: evidently Sulu was born in 2237, and Uhura in 2239. He might then have more time in grade, at which point the chain of command would be Kirk, Spock, Scotty, Sulu then Uhura.
Also, it’s worth noting that Star Trek Online depicts Uhura commanding a watch during the episode “Journey to Babel”: when your PC visits the bridge, she’s in the center seat.