Yes, a schedule of three twelve-hour shifts per week is a common full-time schedule for hospital nurses.
At my hospital and many others, we do self-scheduling, which means that we submit the days that we would like to work for the upcoming month. There are some rules about the minimum number of weekends and holidays we have to work, but outside of that, management can usually accomodate our self-schedule without too many changes.
Some places use matrix scheduling instead of self-scheduling. I don't know a lot about that, but basically, it involves working a set schedule rather than one that resets every month. While you don't pick your days, you know months in advance if you have a conflict and need to arrange a switch with a coworker.
Flexible scheduling can definitely be an advantage of working in nursing.