It depends on the performer and the show. When I did parades in MK, the typical day was: Day Parade, HoeDown, Spectro. A lot of times the people who did the castle show would then come do Spectro. I was trained in Celebrate the Season (Castle Show) over Christmas and I would do the day parade and then the show.
Another popular one was day parade at MK followed by Fant at DHS. Or you might do Jammin' Jungle at DAK into Spectro or Fant. The non equity performers move around a lot more. Most shows have a variety of equity and non equity. The "players" in Festival of the Lion King are character performers for instance, but the singers, birds, and fire eater are equity.
Basically, equity include anybody who does live singing, stunts, acting, or a certain level of dancing. Equity may not move around as much as characters do. I know for Celebrate the Season, a lot of our equity dancers were brought in specifically for that show. Character performers can be equity subs, but it's not that common.
As for working other areas, it is possible. Fantasyland allowed me to work there when I did my entertainment programs. They simply recertified me on my rides. They even trained me a complex I had not learned, but I don't think that's normal. We also have specific times of the year when people work at other areas. These are typically management and we call it "cross" something (sorry, I'm blanking). Like you might have managers stroller parking at Small World.
The other way that you can work other areas is through the Extra Hours Hotline. There are a limited number of shifts that do not require specific training. I used to pick up a lot of shifts filling drinks at quick service locations.