Hi E,
Hope all is well and good luck at the event.
Before I answer your question, I have one for you to consider, please ask yourself this. "What do you REALLY want to know about the job and/or the office specifically?". Once you answer that question, you have your answer to your first question. In my opinion, the worst strategy at these events is to "prepare" questions that you are not interested in, to look interesting to the recruiters. These are people that deal with different kinds of people all the time in different settings, so they can smell "fakeness" from miles away. They are looking for authenticity and real interest for the job. So if you have a question (doesnt matter what it is really) that you really want to ask and you authentically want to know the answer, ask that, you will look better than most people around you that "prepared" their questions, and once their question is answered they can not follow-up with another question/comment and build an ACTUAL relationship with the recruiters.
To answer your second question: Other than questions with obvious answers that you can find online "i.e. what are the application deadlines, can I apply to more than one office etc." you can ask anything. Think about it, as a consultant your job will be to ask the right questions so dont be afraid to ask.
With regards to making a distinction between different roles: If I were you, I would go and speak with the person/recruiter nobody else is speaking with at the event. A senior partner will have 50+ people around her/him looking to impress her/him BUT a) There are at least 2 or 3 steps they need to go through before they can speak with her/him at an interview AND b) Her/his attention span will be so small that she/he will probably not remember you 5 minutes after the event. However a fresh BA at the event, if you impress her/him and show that you are genuinely interested and have the skills, trust me on this she/he will recommend you to that Senior Partner later during the day.
Good luck and just be yourself.
(edited)