What should a conversion candidate expect in a Reform three-judge rabbinic court (Bet Din)? I was told it was to determine the Jewish knowledge of the conversion candidate, but do you have any examples of questions they may ask?
I'm a layperson (not a rabbi) who's spoken with and helped teach Reform conversion candidates. This answer is based on that experience; see also the CCAR's guidelines for conversion.
The beit din will, nearly universally, require successful completion of an introduction-to-Judaism class early in the process (~3 hours/week for 6 months or so). This class covers key observances (Shabbat, kashrut, tefila, holidays, etc), ethical mitzvot, communal obligations, and history. It may also include direct torah study, but my understanding is that this is mostly done in the congregation or with one's rabbi, not in the intro class that's a little more "nuts and bolts".
In addition to the class the candidate will meet, probably weekly or biweekly, with the sponsoring rabbi for personal instruction. This is where a lot of theology, philosophy, and torah get covered, and is usually a discussion (with the rabbi probing the candidate) rather than the "frontal presentation" of a classroom. The candidate is also expected to participate regularly in the congregation. (Also, somewhere in there, the candidate learns basic siddur Hebrew.)
So by the time the beit din is convened, the sponsoring rabbi is already pretty confident that the candidate meets the knowledge requirements (and will have discussed this with the other rabbis on the beit din). Locally (I don't know how common this is), there is also a written exam that is submitted before the beit din convenes. So most of the time with the beit din isn't spent on assessing knowledge, because that's already been covered.
What do they spend the time on? Anything that is a particular concern for a given candidate (special family situations, etc) will be addressed, but beyond that, areas of questioning are likely to include:
Why do you want to do this? What's wrong with being a righteous gentile?
If the candidate is an ex-Christian, questions about giving that up, probing for what the candidate really thinks about Jesus, relationships with Christian family members (e.g. parents), etc -- making sure the candidate doesn't have some idea of "doing both".
How do you plan to observe Shabbat? How will you resolve conflicts between that and your job, your family (if applicable), etc?
Discussion of dating/marriage plans, avoiding intermarriage, and raising children.
(There's probably more, but those are the areas I know about.)