Currently i've got 11 buddies and i wanted to add another one. LfsWorld says it had been added to my list, but it's not listed there. So i thought 11 buddies is the max you can have and i tried to delete one of them, but i didn't find the delete function. Does it even exists?

imho there is no max for the buddy list.

to delete a buddy: LFS Racers Database -> Your Profile and click a buddy you want to remove (first option in selection menu)

Maybe the buddy was added but isnt online (and thus not shown in the Live Alert window)?
If a buddy is NOT shown in the list which you find when you follow 3j's description, it must be a browser Problem (cookies?) or even a bug.