I also had auditions for two different characters on the new Cohn Brothers film, a new Marvel series, several other TV shows, and a commercial.
Should you ask questions at the audition?
In many of the auditions, I didn't get more than the sides (a page or two) and there were a bunch of questions I had about what was going on in the scenes. Do we ask the casting director all those questions when we get to the audition? Nope. If they ask if we have any questions, what they really mean is - do we have ONE question that we really need the answer to in order to do the scene. You can almost never ask all your questions, or discuss the character's motivations, etc.
So, what do we do? Well, I'll pass on what I do. I make my own choices. How do I know if they're the right choices? Honestly? I don't always know. But I make the best choices I can with the available material: who am I?, who am I talking to?, what do I want from them?, where is the scene taking place?
What if I make the wrong choice?
If it says that I'm angry, how angry am I? Sometimes our dialogue will give you a clue, and sometimes we just have to make our own choice. And usually, if it's too strong (and it's better to be too strong than too weak), the casting director will have us do it again and take it down a bit. That's what happened in my audition for House of Lies.
I was really energetic on the first take, and although the CD thought it might work, she had me do it again a little less "enthusiastically." If you take the CD's notes, and do it the way they suggest, it shows that you can make adjustments in your performance - and that's a good thing.
So, even if you're not sure that your choice is the "perfect" one, commit to it fully. You (and I) won't always be right, and we won't get some acting jobs because of it, but being weak and indecisive in our acting choices is far worse than making a strong, incorrect choice.
Okay - I'm plugging my ebook again, but it does cover a lot of stuff about auditioning and booking the job.
The Actor's Guide to Auditioning