My goodness, this is quite a rambling question.

If I understand you , you want to know if you can take a small rice cooker with you on a plane. The answer is yes, either as a carry-on item or in your checked baggage, whichever suits you better. Why would you be shocked that it is not a prohibited item? Unless plugged in, a rice cooker is a pretty inert item. Anyway, it does not have to be in original packaging. If in a checked bag, your bag will likely be searched because of the electrical cord. In a checked bag, it will be subject to baggage handling roughness, so wrap it well. I wouldn't worry about TSA or baggage handlers stealing it - rice cookers are not a high-ticket item. If you have it in your carry-on, they may want to open your bag to see what it is - again because of the electrical cord and also because they are not used to seeing rice cookers on a regular basis.

If you are so concerned about theft, why bother with a rice cooker at all? Cook your rice in a saucepan with a cover (the old-fashioned way).

One thing to consider is if you are traveling form the US to an international location, you may need a transformer for your rice cooker due to a difference in voltage in most of the rest of the world.