For the workouts, is it all supposed to be accomplished all at once in the same setting, or is it okay to break it up?
You can break it up if you need to. That's not a big deal, just make sure you get it all in. I have many clients who work full time or work 18 hours a day, or 24hr shifts and they break up their workouts too. You have to find a way to make it work with your schedule.
I work 24 hours on, 48 hours off, there’s no access to a pool and only limited running opportunity, no treadmill, just some free weights and a barbell. Is it doable?
The biggest thing you will need is a pull-up bar of some sort to use at your station. Most of the workouts can be done with limited equipment. Also with the pool situation, I would recommend just doing the swim right before your shift and again after your shift, and a land workout in the middle of your shift. As long as you space it out like that and do all the reps/miles you will be good to go!