(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?"
This question perhaps over-emphasizes what a moderator can do to steer the culture. As a moderator I would act pretty much as I've acted all-along. Our culture has some inertia and all the active users that have been present on MO for a few years contribute to it. At the same time, the culture has always been somewhat fluid and tolerant of different perspectives.
(3) What time zone are you in?
Most often I live on the west coast of Canada. For the next two months I'm in Germany. I also travel to Japan and Australia quite often. On top of that, provided I'm not teaching I keep fairly irregular hours. So I have a fuzzy time zone. When I'm teaching, historically I mostly used MO as a mechanism to ensure my brain is functioning in the morning -- I would always try to answer a question before my morning class.
(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?
Some users are thornier than others. To some extent we have to tolerate that, but there are some firm lines. Generally speaking I think we like to keep things fairly quiet between the moderators and users having issues with the forum. My impression is mostly moderators need only chat with these users, but in rare instances do they take strong actions like suspensions. I think they've handled things quite well so far and I see no reason to change the culture on this.
(5) How would you handle a situation where another mod closed/deleted/etc a question that you feel shouldn't have been?
I imagine I'd chat with that moderator. My understanding is there's a moderator chat room. This might be a good time to use it.
(6) In your opinion, what do moderators do?
There's a thread on this. Basically, moderators are much like any active high-rep user that frequents meta regularly. They have a few added responsibilities and abilities to interact with the site, but by and large they're not very different from many regular users.
(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 feel fine about it.
(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?
I suppose I don't view being a moderator as an "effectiveness" issue. I think people who get a lot out of the forum should contribute to help keep it functioning and growing. That is what I offer.
(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
We've had many conversations about this on the old meta, and I've participated in them fully. In summary, it would be nice to find a way to increase participation but it's certainly not a pressing issue, for all we know there might be perfectly healthy reasons why there appears to be less female presence on the forum. Perhaps compulsive MO use by male mathematicians is a little bit unhealthy? I was talking with a very strong female mathematician just yesterday and she made the point that she does not want the expectations to compulsively use MO like many of the high-rep MO users do, as she does not like giving the impression that people can just ask her questions on a whim. She objected to the expectation that women should be major users of the forum. She also likes to have big breaks in her day from the math world. This all seems perfectly sane, healthy and reasonable to me.
(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?
Only somewhat. I'm a white male of slavic descent, so by gender/ethnicity criteria I suppose I'm fairly typical for the math world. I do try to encourage people from various backgrounds (engineers, musicians, software developers, etc) to participate on MO and I think anyone who has watched me participate on the forum over these years has seen that repeatedly.
I seem to talk with people about MO quite a bit in person, especially when I visit universities. I've dragged many mathematicians onto the forum, like Ben Burton, Allen Hatcher, Paolo Salvatore and Stephen Bigelow.
By subject area I'm a topologist. While topology is not the dominant topic on the forum, it's one of the more common topics after algebraic geometry.
But I'm not an American, nor a Berkleyite. So that separates me a bit from most of the moderators.