Is it normal that I use nicknames to address people in my family? It's pretty immature since I'm 24, but I like to pretty much designate everyone in my family a special nickname and talk to them in gibberish. For instance, I call my mom "rabbit" or "bunny" and sometimes talk to her using the words "ooh doo" or "joogey woogey.". Sometimes, the nickname alternates to "fuzz face," "furball," "fuzzy wuzzy," "cotton tail," "carrot eater," "carrot breath," "bongo head," "cotton candy," or even "cotton tail." For other people, I generally tell them they are also rabbits, or address them as "scruffy."

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I got it now "fuzz face" =D I like what you did there
I don't really give friends or family nicknames, but I do with kids. Currently, one of the kids I'm working with I call Monkey and I can't really remember why. I also call kids Possum, Munchkin, Poppet, Bubby, and all the usual honey, sweetheart, etc. Despite being taught NOT to in uni. Stupid fuckhead teachers, the kids know their damn names, a nickname isn't gonna hurt.
My grandmother always had rude nicknames for our friends. Maybe that's why I don't have nicknames for friends, unless they choose it themselves :-S
As far as the baby talk, as long as it is kept to a minimum and not done all the time it can be okay. I had a girlfriend that would do that from time to time and it was rather cute!
I forgot to mention that I like to poke and squeeze people on the stomach. Finally, I like to pinch jaws and say "yes you are! Yes your are a yittle wittle wabbit!"
Worst is when someone has a private nickname and you stumble into them as you walk around a corner. With your mind still addled, there's a chance you use the nickname. And yes, I have done. :/
I actually miss Twitter. I know they won't let me re-open my account but I may come back anyway. :)