Coming up with questions about your characters and then answering those questions is an excellent way to develop them very quickly, as you've learned.
As an addendum, I would make two suggestions: one, make sure to focus your questions in a ways which are relevant to the character in question, and two, be prepared to give simple, mundane, entirely ordinary answers to questions even if it doesn't seem very interesting to do so.
Using the premise of your story as a premise for a hypothetical analog as an example, let's say I were to start trying to build a story around the premise of a world which is under assault by some kind of monster and a protagonist who takes up the profession dedicated to destroying these monsters. Just the premise alone prompts questions about the setting and this character. For the setting, questions like "just how much danger are these monsters to the world? Are they going to drive humanity to extinction? Are they a menace to individual towns but unlikely to wipe out all people? Or are they world-eaters, not only ready to devour all humans but also annihilate the entire planet and move on?" would occur to me immediately. For the protagonist, I would first wonder "what motivated them to take up such a dangerous path in life?" The previous question about the setting could open up likely answers to this one. For example, world-eating monsters would make the motivation abundantly clear: necessity. This opens up the possibility for the protagonist to be a reluctant hero, or even a completely unwilling one. If the monsters were not present a threat of extinction, this option for the character would probably not be available. In that case, you would really have to answer the question in a way which clarifies why the protagonist chose to be a warrior when other less dangerous options were on the table.
This is where suggestion two comes into play. It's very, very tempting at this point to say something like "well, the protagonist wants to fight against the monsters because they experienced the generic JRPG childhood trauma of having their hometown destroyed and their parents killed, thus fueling their desire for vengeance against the monsters," and that may seem like a really deep motivation, but on further analysis, it might not be the best choice for character development. You see, in this situation, just like with the character who is required to fight monsters to stave off human extinction, it doesn't really tell us anything about the character's personality, only the necessary courses of action the world imposes on them. A character who experiences childhood trauma is likely to be shaped strongly by it, making it less of a choice on their part to do whatever it is they do. If, on the other hand, you had a character who "always tried to make things fair for everybody" or "got into lots of fights with bullies" and "wants to drive out the mean, ugly monsters," then that tells us quite a bit more about their personality, even though it wasn't necessarily triggered by a deep or impactful event. In the case of a hero who is forced by circumstance or driven by childhood trauma, it doesn't really open up any more questions beyond that. But in the case of the character whose personality drives them to a course of action which others might not take, it opens up more questions and allows more opportunities for probing into the way their mind works. That is how you get your character development going. That is how you make your character an interesting person whose mentality is one which evokes curiosity and a desire to investigate in your audience.
Even the most mundane observations can lead to many questions. Let's just take something simple, like a character with white hair, and start asking questions about it. Why does she have white hair? Is white hair normal for people to have in this setting? If so, that's that, and there's nothing more to it. And that's perfectly fine. It tells us something about the setting, and it establishes that, at least as far as appearance goes, there's nothing particularly out of the ordinary about our white-haired character. Or is this not the case? Is she an albino? Does that have any implications in this setting? Are people in this setting superstitious and likely to take her hair color as an omen or a sign? Or can characters have white hair color without being albino in this setting due to other reasons, like magical aptitude in a fantasy setting? None of these answers, by the way, are necessarily more interesting or worthy than the simple mundane answer of "it's fairly normal in this world and there's nothing more to it than that." Don't be afraid to come back at targeted questions with simple or mundane answers, and don't be too eager to explain every character trait with a deep philosophical exposition. As The Incredibles reminds us, things that are Special and Super experience diminishing returns if they are too prevalent. Try to avoid the temptation to make everything dramatic or unique, because if everything is, then nothing will be. Taking that notion a step further, also remember that - and this is especially true of fantasy and sci-fi settings - just because something is fantastic compared to the setting of our reality doesn't mean it will be fantastic in the setting of your characters.
In short, target your questions, answer them in as much detail as necessary, be prepared to explore several branches of question-and-answer before choosing one, and lastly, never be too afraid of the ordinary to make use of it.