Comments are voted down by other users, not site admins. You don't get this privilege until you have shown yourself to be a good member of the community. This is the one of the key mechanisms that elevates discussions here.

Most stories die because they get flagged by users. Duplicates, things that are boring, plagiarized, etc. Interesting links almost always get submitted multiple times, so it isn't a huge loss to the site if one of them dies unfairly.

Stories can get demoted of the front page by triggering "flame war" like behavior. This is fine IMO because it keeps otherwise reasonable people from feeding the trolls, while the trolls are likely to keep trolling each other (and burning karma) out of public view. The moderator does review at least some of these and fixes the demotion if necessary.

Stories can be manually demoted if deemed "not interesting" by the site admins. This could be problematic, but from what I've seen it is used rarely and reasonably.

There is a proposed thing called "pending comments" which I'm not a huge fan of. I think the tools we have today are good enough and that it unnecessarily burdens the new user experience. IMO people who post low quality comments already get punished by the community at a sufficient level that they either improve or leave. Note that this is theoretical since we haven't seen what this feature looks like in practice.

I do wish there was some more concrete guidance on how the moderation tools were meant to be used (flagging stories specifically) but in those cases you just use the tools cautiously until you have a better understanding of community norms.

Note that I have no affiliation with Hacker News or YCombinator and this solely represents my personal opinions.