Can I put any kind of bowl into a steam/rice cooker?
For the amount of time it will take for this to work, you might as well use the stovetop, which is designed for this -- but if you must, read your manual for instructions on how to use the rice cooker as a steamer. Using a steamer basket inside the cooker pot should work; I'd recommend sticking with just the basket itself if possible; stainless steel is plenty safe. 

If you are going to put a bowl or dish in there, use ceramic or stainless steel - both of those should be fine, and unlikely to leach strange things into your food. You might be able to use some plastics, but I'd think that heating up plastic with your food in it is more likely to put stuff you don't want to eat into the food than microwaving in a ceramic bowl would.