Side note: Ooo that set alone is a Beast! I worked on the original production at MTW. Don't you LOVE those facings!
Oh the horror of those facings. i still am having dreams that my crew couldn't get them on in time. Luckily they during the shows they made it. We cut the number of times we were originally going to switch them out after we figured out how trouble some they could be. The castle was our biggest beast as you can imagine.
Sorry, CO2 does not work like smoke from a smoke machine. It's heavier than air so it will roll along the ground. not float around in the air. And as to whether it will set smoke alarms off, well, mostly they tend to be in the roof, so that is probably correct (the gas won't get to the detectors) but there's no guarantee. And it can cause problems if you have an orchestra in the pit, because it'll roll off the front of the stage and drop into the pit, meaning you run the risk of the musicians a) not being able to see their music, or b) and this is worse, if you have enough CO2 it can cause breathing problems, if they can't get above it to breathe air.
You can get CO2 to work like smoke it all depends on how you have it coming out of the container you are putting the water and dry ice in. If it come out of the container from a 3" pipe its going to flow out and roll. if you reduce the pipe diameter it will pressurize it and it will shoot out of the pipe. you have to be careful that you don build up too much pressure though or you could blow the lid off your container. also there are CO2 cannons that they use in rock concerts that blast CO2 in the air.
Yes you have to worry about the risks of cutting a lot of the Oxygen off from performers or the Orchestra but for the amount of time this effect will be needed (30sec or less) the risk is less than say you are doing a show where a performer comes up out of the ground that is covered in dry ice fog. (if any one has seen "Sing Faster" where they had to build oxygen tanks in to the set for the performers because they were using so much dry ice fog you know what I mean)