For home buyers, I think that questions related to how this agent is going to work for you are the most important.
As you probably know, a buyer's agent gets paid her/his commission at the close of the transaction. This commission comes from the seller, not from the buyer.
That being said, you want to know how this commission based agent is going to find you the best property that fits your criteria. Here are some of the questions that I've been asked or that I've talked to previous buyer clients about in order that they got some of the vital information about the realtor/client working relationship. For me it is important that clients what my business philosophy is and that it meets their needs.
Are you in this with me for the long haul? If I it takes me 6 months to a year to find the right place, will you still work with me? (KEY: Look for commitment)
How much contact (i.e., frequency) and in what format of communications (e.g., email, text msg, and/or phone) should I expect from you. (KEY: Look for what fits you the best and how you like to get communications. Also, it tells you a lot about how they communicate too and their flexibility)
Give me some examples of your negotiation skills or past client negotiations that you've undertaken on their behalf and what was the outcome? (KEY: This should give you an idea of how they think and how they work for their clients)
What has your client base been like? What types of people have you worked with in the past? (KEY: This will provide you with an understanding of what people have gravitated to working with them in the past, also the calibre of people that have been attracted to working with this realtor)
What's your experience/work background? How has that helped you in the past with your clients? (KEY: This should give you an idea of their professionalism)
Alejandro, I hope these help to some degree. Best wishes in your interviewing process!