A note up front: these answers may be copied and modified from my earlier nominations. Most Stack Exchange communities aren't that different from each other, and I still stand behind answers I gave in the past.

1. 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?

Being nice is very important to the success of Stack Exchange; more important than posting good answers (or questions, for that matter). I'd remind this user (in a polite but strict way) to change their behaviour or face the consequences in the form of a suspension. There are enough other users who can write those valuable answers instead.

2. How would you handle a situation where another mod closed/deleted/etc. a question that you feel shouldn’t have been?

I'd discuss this with them in a private chatroom. I might bring in a third moderator as well if I feel we need to make a tough decision, so that it can be a decision of a majority. There's no need doing this in public and risk harming the trust the community has in the moderator team.

3. In your opinion, what do moderators do?

Moderators are first and foremost elected by the community to represent their interests in every way possible. In general, those interests may be helping with welcoming new users, handling flags, doing a lot of reviews, and being a bridge between the community and Stack Exchange the company, among other things. It sometimes means putting your own ideas second, third, or even ignoring them altogether. Writing answers (or questions) is not one of their primary tasks; that's where subject matter experts are for. Hence my nomination :)

4. 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?

No problem at all. I always try to Be Nice to all people, even if I think they have bad ideas or opinions which I can outright refute. Respect is the keyword for building a community where everybody is welcome. I have certainly made some mistakes in the past, but that only proves I'm human ...

5. In what way do you feel that being a moderator will make you more effective as opposed to simply reaching enough reputation to access moderator tools or become a trusted user?

Moderator votes are binding, which is handy to quickly get rid of content which doesn't belong here.