Has anybody studied the shortest possible mating sequences from various Chess960 starting positions?
 
I just saw this, with starting position NRNBKQBR:
 

1. d4  e6
2. c4  Qb4#

 
which is really the same as standard chess's fool's mate, just on different files. From some positions, it's possible to mate on white's second move, e.g. for RBKRNQBN
 

1. e4    b7
2. Qa6#

 
I suppose the questions are:
- What is the distribution of the lengths of minimal mate sequences among the 960 starting positions?
- What position has the longest minimal mate sequence?
- Are there any mirror-image positions that have, because of different castling options, minimal mate sequences that aren't just mirror images of each other?