How to bake bread and desserts without an oven?
From your list of 'electric stovetop, pots, and rice cooker' I would suggest constructing a double boiler by placing one pot inside another where the inner pot has a lid and the outer pot has a measure of water sufficient to support the inner pot (a steel bowl would be preferable, but you didn't mention that). Using a low heat (just enough to bring the water to a boil). Place your product inside and be prepared to wait. The double boiler will closely resemble oven like convection to evenly (albeit slowly) heat your food. It should brown well and you minimize the risk of burning. If you are making something like a small pizza, you should definitely add a small bit of oil/butter to the bottom of the inner pan.

Do you have access to a 'slow cooker' (crock pot)? These can be used to create a variety of 'baked' goods (breads, pizza, cakes...) But I am guessing not (because you didn't list it...) However, you do mention a 'rice cooker' which is not that different (depending on the brand/style) and I would be inclined to experiment with that.