1. What do you think the main job of moderator is?
A moderator should be a leader first and foremost, someone that the community should look up to and admire. A moderator has the job of gently but firmly guiding the site in the right direction, while resolving interpersonal disputes and off-topic debates along the way.
2. Do you have any previous experience as a moderator?
No, I'm not a moderator on any other SE site. However, I think that I've been around the network long enough to know more than the basics so I am very familiar with different moderation tools.
3. Our site is a very new one. We can expect a lot of posts that are broad, but are about practical problems faced when learning a language. What is your opinions on such questions?
I definitely would not turn away these users and their questions, as denying them on the spot is like a frigid blast of cold air; it pushes the user and any potential contributions to the site they had away. Rather, I would help the user reform their question into something that can have a less narrow scope, thus making the question far more answerable and welcome on Language Learning.
4. If you users fight over each other in comments, etc... how will you handle that situation?
I would take a firm stance against harsh arguments and fights in comments or chat. I would first warn each user involved in the argument privately in a chatroom, then if the troublesome behavior continues, I would suspend the user(s). First and foremost, there is a person on the other side of that screen.
5. Some users who post great answers may not agree with the community. For example, they may ask a question which was previously agreed to be off-topic and may want to include such questions as on topic. How will you deal with such users? We surely don't want to loose such users and their good answer.
We don't want to lose these high-rep users, but at the same time, just because they've been around a while doesn't mean that they can get away with changing the scope of a site. The site's scope of on-topic questions has been agreed upon by the community, so if I did see a high-rep user repeatedly asking decidedly off-topic question, I would try to revise the question to fall within the scope of our site. In addition, I would try to collect feedback/thoughts of the user on the site's scope. If there is a valid point in changing or slightly modifying the scope of on-topic question, I would start a meta discussion and see what the community thinks of the suggestion.
6. You come across a question which you think should be closed. But major of the community people say the opposite. What will you do?
In this situation, I would generally agree with the major members; after all, (almost) everything about this site (including the scope) is decided and agreed upon by the community. As such, in this case, the community's decision is my decision.
7. If a fellow moderator disagrees with you, how will you handle that situation?
I highly doubt that this will ever happen, as most of the people on SE sites are very good-natured and cooperative. If such an argument did happen though, I would have a civil discussion with the moderator in question in a mod-only chatroom so we can come to a consensus. If things get really out of hand, I would pass it up to the Community Managers to take care of.