Negative Karma is generally not used by moderators (only rarely), negative Karma is more used by users who have no other tools, they only use Karma and report users/posts. On the other hand, moderators do have other tools, such as monitoring (Watched) a user for a certain period of time, in order to monitor the next steps of the user who violates the forum rules.
In response to the second paragraph of your post, there are users who have badges but do not have negative Karma because of what I have explained before, moderators do not usually use negative Karma for that, they simply give the badge that is necessary for that case.
These tools would be very helpful for you? Other than badges if allowed what other tools moderators are provided with. I thought he was given negative karma is from moderators because most of them have only 1 negative karma.
It might of been to be honest. Unlike freemind, as well as other mods, personally I distribute a reasonable amount of negative karma to shills, plagiarists, spammers, shitposters, and the like
(shock horror) when punishing users. Granted it is somewhat irrelevant if you're dishing out a shill or AI badge, but for me it's just been a habit for a long time prior to having these badges (before we just had moderation groups mainly, so seemed more relevant). I don't think it's right or wrong to distribute -karma either, that's up to the user to decide, and for mods to determine whether useful or not.
They don't even have 2 negative karma so I took it as a symbol and when whenever I saw a memebr with -1 karma I think he must have done something wrong like spam etc. I must change my judgement.
Freemind is right that the -karma could have come from anyone, as any Snr+ member is eligible to distribute.
It didn't necessarily come from a mod either, could have been d team or otherwise.