I was asked if I wanted to throw my hat in. No. I am a newbie and shocked it was just based on points. I have 706. The rep needed should be way higher! What I want to know is, 1) are current mods up for reelection or secure in their positions? 2) Do you have to nominate yourself or can you nominate someone else? Again 706, I will let you decide, but I am curious.
This election is to add one moderator to the existing team; no moderators are being replaced.
Candidates must self-nominate. If there is somebody you think would be a good candidate, you'll need to ask that person to nominate. Chat is a good place to do that.
While SE only requires 300 reputation to stand in an election, the practical limit tends to be a lot higher, as you've noticed. But better to set a lower boundary and let each community decide than to set a higher one and shut out people who, under some circumstances on some sites, would be good candidates. Throwing your hat into the ring is relatively easy; persuading the community to elect you is the bigger challenge.
Although I have been here for a while now and kind of familiar with the place, I still don't know answers to some of the questions you have asked. (I am more concerned with answering people's questions to the best of my knowledge, instead of learning the mechanics of this site). I will still try to answer your questions to the best of my knowledge.
1- The current mods are not up for re-election, this election is just here to add one person to the group.
2- You have to nominate yourselves. You cannot nominate anyone else. Although I would love it to be so that nobody can nominate themselves and people could only nominate others. That would help produce more productive mods with higher member support.
3- Although it is not a part of your question, but I should add in that 706 rep means that you know how the site works. That is enough for your experience with the site working, to serve as a mod, if you want to run for it. Also, while 706 is indeed very low rep, considering that the site is run by the community (or so we like to believe), if the community wants a 300 rep mod, why not?!