The Administration deserves more writing than it currently has in terms of pinning down it's structure and goals, but striking the correct balance is always on the fore of my thoughts and to a large extent I do want this sort of exploration to be table-specific and fit the desires of a given group... similar to how big-picture questions about the nature of, say, Leviathans or the Immortal Emperor are left up to the table to decide upon (or ignore) in Blades. It's very possible for a crew to go many sessions without interacting with the Administration (unless they're actively seeking them out or doing a LOT of high-intensity scores that send them shooting up the Chaos track), and by the time they do that group may have a stronger individualized idea for their conception of World and what Admin needs to be for them.

As was true in Blades, a favorite GMing technique of mine is to solicit guesses or ideas from the whole table of players, as the discovery of your version of the setting is best done in a collaborative format. Not all questions in a Forged in the Dark game are best answered in the text.

What you do with the Board is up to you (and I would also hope the player who takes that Special Ability gets input of their own), but the origin point of the idea is inspired from the video game CONTROL. In case you haven't played it, and you're comfortable with light spoilers for an action game from a few years ago, the following article does a good job summarizing the presentation of that game's "Board"  as well as one very reasonable interpretation of it's themes: https://www.vice.com/en/article/j5ypj3/control-the-board-pyramid