"Continuing from your (really awesome) explanation of ranks and billets. How would it be like with shifts. For example, Sulu can't be on the bridge 24/7 because he'd have to eat, rest, take breaks, etc. How does that work with the organizational system of things?"
Thank you for the compliment! And good question.
I believe starships work on 3 shifts per day (assumed 8 hours because lets be really, no one wants to get messy with other-houred days and Starfleet is still Earth-Human Dominated) : Alpha, which runs 8am-4pm, Beta, running 4pm-12am, and Gamma, 12am-8am.
Generally, we see the primary Bridge crew all on the bridge together. I personally have always run off of the assumption that they are the Alpha shift crew, as that is kind of the nicest time slot. There are then alternate crews for the other shifts. An alternate pilot would come in and replace Sulu, someone from the science department would replace Spock at the science station, Uhura would have a replacement come in from communication, and so on. Even Kirk would have a relief, someone else from the command department. Alternatively, Spock could be Kirk’s replacement, working a double shift. Then those replacements would be replaced in turn by the Gamma shift bridge crew.
Who is on those crews would be chosen by the different respective department heads. So, Spock would set up a work schedule for science people, Uhura would assign different com officers to relieve her, etc. Kirk would handle the general stations - navigation, telemetry, piloting - as far as who was working when.
I hope that answers your question. Uh, take it with a grain of salt, as I haven’t done a ton of research on that aspect of ship life, but it seems the most logical solution. Though there might in fact be more than 3 shifts, maybe four, and perhaps Starfleet ships don’t run on 24 hour days. If anyone does know for sure, please let me know and point me in the direction of where I can find the information!
As pointed out, if the Captain is off ship and an emergency happens, they can emergency recall him to the ship, provided he is not the cause of the emergency and can't be pulled out.. But generally, if there is an emergency, the captain and senior crew will be heading to the bridge, provided they can get there. Or the auxiliary bridge.