You should only give Karma for specific reasons. If a user has 0 Karma, just report them (bottom right of each post) with a message to give them Karma. As a mod you can only give/take one Karma per hour (and you should post why in the precedents threads)
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BTW I tried to give karma to a user who have 17 post but 0 karma, and the system (like you say) permits me to give only 1 karma at a time, and I need to wait 1 hour between points. The user is "Maverynthia".
Nope, I don't have those buttons The only "different" buttons I see on the forums I moderate, is the "Split Topic" button. Let me know if you can find something about it.