I saw someone else make a list of these, so I thought I might as well post some more. Feel free to add your own in the comments! Also, credit to @LilNerdyGingerKitsune for questions two and three.
If this character found their crushes diary, would they read it?
How do they feel about snow?
How long do they take to shower?
If their child self could see them now, what would they think?
if they could give themselves a superpower, what would they choose?
How complicated is their usual Starbucks (Or any coffee shop) order?
What's their favorite candy?
If they were arrested, what would it be for?
What's their biggest pet peeve?
What type of outfit or piece of clothing would they never wear?
What's the most embarrassing thing that's happened to them?
Would they eat an octopus (If given the chance)?
Are they allergic to anything?
Do they keep any collections?
How good are they at remembering things?
Did they have any imaginary friends growing up? Do they have any now?
What's something they've always been bad at?
What are their triggers?
What do they think is their biggest flaw, and what's really their biggest flaw?
If they could go anywhere in time and space, TARDIS noises where would they go?
Do they still sleep with a stuffed animal? What animal is it? Does it have a name?
How terrible are they at babysitting?
How good are they at gardening?
How skilled are they when it comes to cooking?
What colors do they think they look best in?
If they could change one thing about themselves, what would they change and why?
What type of music do they like?
Have them describe their favorite memory.
Have them describe their least favorite memory.
If they could learn any language, what would it be?
You describe them in three words. Now let them describe themselves in three words.
If they were given an unlimited amount of money, what would they buy first?
How do they feel about children?
How do they greet people? Do they wave? Shake hands? Give hugs? Fist bump? Does it depend on the person?
Do they believe in talent?
Have they ever been on a date?
How terrible are their flirting skills?
What's their sense of humor?
Have them describe their favorite and least favorite people.
If they could forget any memory, what would they forget?
Do they like puzzles?
Imagine them in an escape room. How do they react?
Do they get really emotional over fictional characters?
What's their favorite subject to talk about?
When they're hurt (physically or emotionally), do they try to hide it?
What do they think is a waste of time?
What's their favorite ice cream?
Have them confess something really dumb in a very dramatic way.
If they're called out for lying, how do they react?
If a stranger calls them hot, what do they do?
How do they react to compliments?
Imagine Disney movies exist in their world, which is their favorite and why?
What's something you believe that they disagree with?
What do they think about miracles?
If they were to play a prank on someone, who would they choose and what would they do to prank them?
What do they think is the evilest thing a person can do?
If they had a child, what would they name it?
Is there anything they would trade their soul for?
What's their deepest, darkest secret?
If they were a ghost, what would they haunt?
What are their unpopular opinions?
What I did with these was I made a category called "Character prompts, asks, and questions" to my Characters page and slowly added each one, but you could just answer them in your head or comment your answers. Hope this is helpful!