Here are my answers to the questions.
These are my personal views from a practical point of view on this site and may or may not reflect any official guidelines.
The answers to different points are independent, so feel free to skip to what is relevant to you.
What actions would a moderator be expected to perform on a regular basis?
Checking that all is well.
If there are new meta questions or flags, the top bar will show them in a separate moderator inbox of some kind.
Also regular messages (like comments and chat pings) are good to check.
Additionally, it is good to check that the recently active posts look fine and users are welcomed and instructed appropriately.
Most of this is no extra work if you follow the site anyway.
(There are also some things moderators are unfortunately not notified about, such as incoming migrated questions.)
I think the only thing that must be done is seeing messages directed at moderators and acting if necessary.
Most things are not urgent, but some are.
There are things on different time scales.
The ones I mentioned here are the daily business.
Long-term ones include learning more about the site's functionalities and checking whether known problem users have been up to anything nefarious.
Discussion with other moderators within and without this site and coordinating efforts is also good.
How often are they expected to take these actions?
Depends on the task.
If at least one moderator checks in every day to take care of anything urgent (which does not happen every day, far from it), it's fine.
If, for example, you can spare 10 minutes on most days and 30 minutes once a week, it should be enough.
If you are an active user of this site, there is no need to increase your visiting frequency just because you become a moderator.
Our site is pretty relaxed and moderator work is a minor chore.
Is there an SLA for how quickly they need to be completed?
At the moment we often leave flags hanging on purpose.
For example, if a new user posts a bad post, we will leave a comment requesting improvements and delete the post in about two days if nothing has happened.
Leaving the flag active makes it easier to follow up on things, and I quite often flag posts just so that I can follow up on them or point something out to my fellow moderator(s).
If there is something more urgent, like a post getting a lot of spam or a user harassing others, then acting quickly is a good idea.
But it's never a matter of minutes.
There are ways to freeze things in place if that is needed.
Much of the moderation is handled by the community.
If enough people vote to close or flag a comment as inappropriate, automatic action will be taken.
Moderators don't have to run things, only check that they run well.
What kind of background is needed to be a good moderator? Should I be fluent in Latin, an experienced user, or have any specific skills?
A moderator should be familiar with our community and willing to help it.
There is no need to be an expert on the subject matter.
While I think it is good to have at least one moderator with decent Latin fluency, not everyone needs to have it.
(I don't understand much Greek, and that has turned out to cause zero issues in being a moderator.)
Different SE sites and especially different websites have very different cultures, so familiarity with our site is important.
If you want a quick rule of thumb, users with over a thousand points on this site have enough knowledge, experience, and activity to make a moderator.
The key skill set is not in substance but behaviour.
I expect a moderator to communicate clearly and behave well.
If you get angry at something on the site, let the steam out in another way before touching your computer and take action when you have calmed down.
Small conflicts arise every now and then, and you should know how to deescalate rather than escalate.
What tools do the moderators have?
There's plenty, but there's some merit to not disclosing them all to the public.
There is a whole page of moderator-only tools, and moderators have access to much more information.
Moderators can also contact users privately and they have their own private chat rooms.
Regular tools work a little differently as a moderator, but no tools are lost.
Do moderators work alone or together? Can they get help?
Simple matters can be handled alone and some urgent matters cannot wait.
Deciding what to do with a specific post/user/pattern/phenomenon is a common discussion topic in moderator chat rooms.
Discussions help keep the policy uniform.
In addition to fellow moderators on this site, moderators can ask for external help.
Things can be escalated to SE employees if needed.
There is a separate hidden Q&A site for moderators.
There is a chat room for moderator discussion between different SE sites.
The mother meta is a good place to ask questions about the site's functionality.
How does being a moderator change the normal use of the site?
Not much, and that's the point.
Think of a moderator as a janitor who is also a regular user of the building.
All users can play a role in moderating and leading the site, and becoming a moderator does not mean that you would have to take on a particular role.
I find it important that a moderator does not just act from an ivory tower; they should really be citizens among the others.
The one limitation is that moderators cannot vote on anything related to moderation.
(Voting on questions, answers, and comments work normally!)
If a moderator votes to close, the question is closed immediately.
If a moderator flags a comment, it is deleted immediately.
If a moderator reviews something in the review queues, it is dequeued immediately.
There have been cases when I would have voted to close a question but did not because it would have closed it unilaterally, and I often wait for other votes to come in so I know the action has support.
If you are currently a moderator of this site, what do you enjoy most about moderating, and what would you appreciate more help with?
I enjoy seeing the site thrive and I am proud to have helped it do so in my small way.
But most of all I enjoy using the site as a regular user, and moderation comes on the side.
We currently have only two moderators, and the biggest (but not big or urgent) downside of that is the difficulty of having discussions.
We agree most of the time, but there is no clear way to decide things when we disagree.
A third person would bring more perspectives and break ties.
The least enjoyable thing — which I think is inevitable and do not expect help with apart from discussion with colleagues — is making decisions that have negative effects on others and confronting problematic users.
Sometimes a user behaves so badly that someone has to step in and ask them to stop.
Regular users can choose to disengage, but one of the moderators should go and do it.
The user might lash out and protest.
The user might have to be suspended.
Feelings may have been hurt.
Fortunately these scenarios are rare and problematic users are very rarely valuable contributors.
Sometimes keeping the site welcoming and good-spirited requires closing some actions and users out.
What kind of relationship or contractual obligations will I have with Stack Exchange?
There is a moderator agreement, but it is mostly about being responsible with the increased powers and continuing to be nice to other users.
Following and enforcing network-level rules to the letter is not something you need to commit to; a moderator's commitment is to supporting a socially and technically functioning site.
A moderator is much more a representative of the users of this particular site than a representative of Stack Exchange.
There are network-level structures that are helpful to a moderator, and a moderator should certainly be collaborative towards employees and fellow moderators.
But there is no contractual relationship and this site can be run pretty autonomously as long as no trouble ensues.
So far the site has been around for about five years and there has never been trouble between our site and the network and I don't consider it a likely scenario for the future either.
If you want any more details, leave a comment here or add more specific questions to the original post's list.