Still waiting for an email explaining anything
You should receive a reform card with chat logs upon logging into the client as well, if you were punished by the Instant Feedback System for chat offenses. If you were not, then you need to submit a Support Ticket for more information. Make sure your email is verified by clicking your profile on the top right of this page and going to Settings.
a report from a group with a racial slur as a group name isn't permabanned
I believe those are handled manually. You will not be informed of what actions they take against those players, but rest assured that they do take it seriously.
after reporting someone else, which you would think would trigger a check on the reporter as well
Why would the system check the reporter as well? They will be treated the same as you by the system, given the same leniency and the same chances to change. Just because one player is punished doesn't mean everybody else needs to be. You're looking for vengeance, not justice.
Is false reporting not an offense or something?
False reports don't hurt you, so on your end you don't need to worry about them if you did nothing wrong. On their end, they will lose report weight for making them.
telling someone off is instaban worthy
It depends on what you said. Only the most extreme offenses skip punishment tiers, but otherwise you are given multiple tiers of punishment before ever reaching a permaban.
Who even bans for a curse word?
I still don't have context from any prior punishments you may have had or what resulted in this ban, so I can't properly answer why you got permabanned until you come back with that information. As for curse words, those are not the problem; it's the manner in which you use them. I can say "fuck" all day, but it doesn't matter (short of spamming it of course). When I start saying "fuck you noob" it is a different matter because I am directing it at another player, especially in a hostile manner. You don't get permabanned just for saying "fuck" etc. once.