...as Columbo used to say. Someone emailed me and asked, "Is it okay if I come up with more than twenty questions to get a handle on my characters?
Sure it is. You can come up with hundreds if you want. It's your book.
Only caution: Don't get so wrapped up in backstory that you forget your main goal - to write a book.
As for other questions, deal with things that lead into problems: What does the character do for a living? What does the character hate about that means of earning money?
If the character were truly desperate, what moral absolute held dear by the character might be bent or broken? How would the character feel afterward?
Stress. It's all down to stress. Jane Yolen, a lovely writer, once said "There is only one plot: Joe gets his ass caught in a bear trap and has to get out."
When you know your character thoroughly, all the background, habits, ways of thinking, philosophy, beliefs, you can really put that person through the wringer. Don't make it easy. Make it hard. And then make it harder.
And you know what? You're going to wind up with a story worth reading. So, yeah, come up with more questions. Knock yourself out. But when you get to the agonizing decision your character might face -
Stop. And start writing the book.