(1) For pseudonymous candidates, Are you a professional mathematician? In what capacity?
Not applicable. (I am a professional mathematician, working in academia.)
(2) Assuming a notion of "culture" as explained here, what would a newly elected moderator do to preserve it? Will there be more efforts to preserve the culture, or more to steer it toward things nearer to "what a Stack Exchange forum should be?"
There are several aspects of this culture that I appreciate very much, and clash somewhat with the culture of other Stack Exchange sites I frequent. I hope these are preserved, and there will be no encouragement of my part to change them. An example that Gerhard mentioned explicitly is wordy comments. Another seems to be the treatment of CW soft-questions, of which we have many excellent examples; we do not want these questions to overrun the site, of course, but the good ones have proved quite useful. I hope to help maintain the site standards, and the best way to do this is through example, in the posting of thoughtful questions, answers, and comments. I also appreciate how meta works and allows the whole MO community to become involved, with vivid exchanges we see in comments. This thread I started to request reopen votes is a good example; the community clearly appears to appreciate it and use it, even though its approach seems discouraged by the SE system, as it was pointed out in comments.
Naturally, if it becomes clear that something we do in the site is not as effective towards our goals as it would be if we followed the model of other Stack Exchange forums, I would be supportive of that change.
And I hope I will be attentive enough to hear suggestions of other participants and colleagues that may help improve our experience.
(3) What time zone are you in?
Mountain Time Zone (Currently, UTC$-6$).
(4) How would you deal with a user who produced a steady stream of valuable answers, but tends to generate a large number of arguments/flags from comments?
I expect these users would each pose unique challenges, and an all-encompassing policy may not be the best approach. When in such a situation, I would attempt to reach a consensus with the other moderators before proceeding. First, I would familiarize myself with the policies the current moderator team follows. This team is quite thoughtful and I expect they have experience with these difficult situations. We would then contact the person privately and explain the problem, hoping a solution can be reached with minimum conflict. If this proves insufficient, and the policies in place do not seem effective in a particular case, we would seek advice from the Community Managers.
(5) How would you handle a situation where another mod closed/deleted/etc a question that you feel shouldn't have been?
I would contact them privately (in a way that all moderators see the exchange and can participate), and would explain the reasons why I believe the decision was incorrect. I would ask them to reconsider that decision, and would try to start a dialogue leading to a common decision on how to handle similar situations in the future.
That said, I expect to be open to be persuaded and change my viewpoint. Something I would definitely not do is to unilaterally undo their decision.
(6) In your opinion, what do moderators do?
Moderators help the community be informed, by answering their questions about the site, and providing assistance if needed. (Beyond matters that affect the whole community and are discussed on Meta, I have particularly contacted the current moderators on several occasions asking for clarification of site policies, or statistics that I have needed, etc, and their responses have been not just efficient but very useful.)
The cleaning of flags seems to be the busiest activity, perhaps followed by the removal of off-topic posts (of which we have periodically quite a few).
Moderators deal with problems that may appear within the community, helping it stay a civil and inviting place.
Some tasks are administrative in nature. In his answers to this question, Scott mentions the legal entity. I expect new moderators would be involved with it eventually as well.
(7) A diamond will be attached to everything you say and have said in the past, including questions, answers and comments. Everything you will do will be seen under a different light. How do you feel about that?
I am fine with it. Of course, it will be a remainder to be thoughtful and measure my actions, but this is something I already try to do. I do not expect it will affect in any way the kind of questions, answers, or mathematical comments I post.
(8) In what way do you feel that being a moderator will make you more effective as opposed to simply reaching 10k or 20k rep?
It is obviously a very different role than as a regular user, which does not mean it would affect my mathematical contributions (such as they are) to the community; MathOverflow is valuable to me beyond words. My being moderator would be a way of further contributing to the site and being more involved, beyond how I interact with it on a regular basis.
(9) Do you think women are underrepresented in the MO community compared to the mathematical community as a whole? Is this a problem for MO? If so, what would you do about it as a moderator? See also: 1483 and 985
It is an obvious problem (not just for MO). Solutions are difficult, short term solutions seem unrealistic. Unfortunately, I do not have a good answer; this is something that I have thought about at various levels for a while.
I hope to help promote the site (this seems particularly important), and to keep it a collegial and inviting place (we can certainly improve in this respect, I know of a few people who feel intimidated about participating).
Female colleagues with whom I have discussed MO but do not participate in the site do not seem concerned with these issues, luckily, but typically indicate that their field is underrepresented; there is the beginning of a good discussion about this here. Some find the reputation system a turn off, though there are workarounds.
Again, this is a serious concern. As a moderator, beyond whatever can be done through promotion, I would be very open to suggestions.
(10) As MathOverflow is growing, the diversity of the moderator team might become an issue of interest. As I understand, the present moderators have much in common, and women are, to say it that way, underrepresented. In which way do you think would you contribute to the diversity of the moderator team?
Though I live in the States, I am from Colombia. Incredibly (I seem to live in denial) I am older than most(?) of the current moderators, and do not know most of them personally. I work in Idaho, at a primarily undergraduate institution, whose population is mainly of nontraditional age and first-generation college students. This provides me with a unique perspective that I expect may prove useful to the team.