Does the admin(s) need to do anything to hide a post when a post has been flagged by users or it is automatically hidden?

It's automatic. If enough users flag a post, it gets "killed" and will only show up (with the tag "[flagged][dead]") if you have the "showdead" option enabled in your profile.

It's automatically hidden.

I don't think it's an awful system but I don't think it's exactly right for HN - in normal operations it works fairly well but when combined with some less desirable HN stereotypes it can just involve shutting down discussion one disagrees with (e.g. merely mentioning Donald Trump by name was an insta flag during the election, but you could always get away with worse if you talked about democrats because the average user is further right than most forums)

I think most of us automatically downvote or flag anything political regardless of personal politics. Especially US presidential politics, because that's what the uninteresting parts of the internet are for.

It is completely false that a bias doesn't come into play with political content.

It is not necessarily a bad thing, but some users appear to have been given more power and can shut down those articles more quickly.

The least bad system is far more transparent.