"Where are the bears?"
When I wrote above 'only when it is "the" something', I was simplifying. Often, a definite object is one with "the" before it in English, but even "this" and "that" are definite, since they are real, defined things - if you say "look at this", there must be something that exists that you can or could point to. This is what definite means. An indefinite thing is usually accompanied by "a/an" in English. If you say "look at a cat", then you're not specifying a particular cat, and it's indefinite.
The concept of definite vs indefinite is a little difficult to understand, and very difficult to explain concisely and clearly, so it's often just better to learn it by learning what is and what isn't definite, and when you have זה in Hebrew, it is always definite, so as an object (when something is done to it), it must be preceded by את.
Yes. In מה הילדים רוצים, the הילדים is the subject. The object, you can say, is "what". Indeed, את מה הילדים רוצים sounds... not quite natural, but almost natural. And if it's מי instead of מה, for example "who(m) do you love?", you have to use את, it has to be את מי אתה אוהב. Not sure why this difference between מה and מי.