Re: diminished arpegios
They are simply fully diminished chords played as an arpeggio. i.e., Fdim7, F, Ab, Cb, Ebb, to be enharmonically correct, otherwise, if you play F, Ab, B natural, and D natural up to F and continue the cycle, you'll be playing the Fdim7 arpeggio. Now, do it in all 12 keys! (There are 12 keys, but only 3 different finger patterns for diminished scales and arpeggios, figure it out!)
PS There are only 3 patterns because after you move to the fourth note chromatically from F, you get to Ab, which is part of the F pattern, got it?