su-doku questions...?

spurred on by occular's post, i decided to try and write my own deterministic sudoku solver. at the moment i'm using java, but i think that prolog or any other AI language would be ideal. anyway, i had a few thoughts while doing this, which i don't know the answers to (yet...)

• how many finished 9x9 sudoku grids are there?
  
• how do you create the starting grids - is it simply backtracking from a finished square that fulfills the constraints?
  
• in connection with the previous, it should be noted that most starting grids i've seen have 180 degree rotational symmetry about a diagonal, sometimes 90 degree about both or reflectional about both, just like crossword grids
  
• is there a way to determine the 'difficulty' of a particular starting grid deterministically, or is it purely subjective?
  

if anyone has any ideas, i'd be interested...