Neil, An inversion is a chord which uses one of the notes other than the root as the bass. For example, a C major chord is C-E-G, and a C chord in first inversion would be E-G-C, in second inversion this same chord would be G-C-E. The little "degree" after a chord symbol does mean diminished, this same circle with a slash through it signifies half diminished.

Hope this helps, it at least shows I've learned something in my Theory classes.