What is the process for making a sudoku puzzle?

Are they reverse engineered, or is there some mathmatical process?

Can the total number of distinct Sudoku puzzles be calculated? Any experts in math stat here? How in the world would you calculate this? I was a math major many years ago, but I can’t quite figure it out. Please post the solution if you can.

A Sudoku-2 puzzle is similar to the usual Sudoku puzzle, except for the fact that it includes 16 squares on a 2*2 board, rather than the 9*9 one, and it’s played in the same way (of course you can only use numbers ranging from 1 to 4). I have estimated the possible results of a solved Sudoku-2 into 4*3*2*3*2*2*2 = 4!*3!*2!*2 = 576 but I have followed a heuristic method and I have not been able to find a way to prove it mathmatically. Is the result correct? And if it is, is there a way to prove it?
Note:
I have noticed that some of you have answered that there is only one way to fill a Sudoku-2 puzzle. This is true if you see it as a game, but my point is to find out how many possible outcomes are there if you fill an EMPTY Sudoku-2 (which means without the given numbers; doing it all by yourself). I hope this clarifies what I asked.

If they don’t fill enough squares, there will be multiple solutions; if too many, either there will be no solution at all (if a conflict arises) or they are making the problem easier than need be. Are there rules that describe the minimum number of filled squares to define a Sudoku (whether 3×3, 4×4 or bigger)?