Jason has given you a good summary of the SE rules on the matter, but what you really want to know is, of course, who did what to whom, without any wrapping of bureaucratic language.
I'm not a mod, so I don't know any specifics of your case, but I can tell you what you need to know about how the suspension system works in general. (And just in case you suspect me, I wasn't involved in any of it; I'd gone to bed by the time all this happened.)
1. Someone flagged you
The comment you made in chat got flagged. Anybody can flag - you don't need to have 10k rep or anything. If there is a rep limit, it'll be something tiny like 20 rep. Impossible to find out who, unless you're a CM: not even mods can tell at this point.
If it was a mod who flagged you, that would have got you a 30-minute auto-suspension. If it wasn't, we move on to stage 2...
2. The flag was validated
Assuming it wasn't a mod who flagged you, the flag needed validation from six 10k+ users (or one mod) in order for you to get that 30-minute auto-suspension. That means six users with at least 10k rep network-wide, or one mod, agreed with the original flagger that your comment was inappropriate. Again, impossible to find out who, maybe even for CMs. Most of the active chat users on SFF do have more than 10k rep, so you can't even narrow the field much.
I'm sorry to see that you've now been suspended on the main site. Without attempting to justify this action, I can't say I'm surprised. SE doesn't tolerate people expressing their feelings in certain ways, and if someone is saying things the moderators don't want to hear, it's always possible for them to suspend you. Suspensions can be reversed, but that happens only very rarely. You will have received a suspension message from either one of the site mods or a CM, to which you can reply if you want to appeal the suspension (or just tell them what you think of them). I wouldn't recommend it though - it's only for a day, and no action is likely to be taken that quickly.
You've already expressed displeasure with the way this site is run and decisions that have been made by some high-up people. Receiving this suspension must have only exacerbated your annoyance. I'm sorry that you have to go through this. I hope we'll still see you around - there are plenty of us on SFF.SE who like and respect you - but I'll understand if you decide not to participate on SE any more after this.