Yeah, a fifteen-fret uke will have two octaves. The lowest note is middle C. Then the E string (open) is the E above middle C, the A (also open) is the A above middle C, then fifteen frets down you have the second C above middle C. That's two octaves.
Yes, peanuts and peanut butter can aggravate arthritis. I was a peanut butter eater all my life, I am now 58.
As far as peanuts go, the protein in the peanut is the trigger and that's another reason to stay away from Peanut oil (in my opinion) is because you never know if it is free of the peanut protein. Cold pressed oil or oil that has been used to cook peanuts may contain peanut protein and could cause a reaction.