I am looking for ideas to improve my Sudoku game in cool ways,
Great touch with the keyboard support, although you should be consistent and disallow keyboard numbers that can't be in that cell just like you do with the mouse approach. To not confuse the player ("why isn't the keyboard working?") you could show the number pressed in red and fade it out.
Also, you could make the number selector slightly larger for mouse selection.
Something I find useful in Sudoko games is annotations, like marking possible numbers without filling in the square (make them small in the corner or greyed out).
For some inspiration on a multiplayer Sudoko game, check out http://www.sudokuandfriends.com/