1. Since you are writing your own version of Tetris, you can make the game dimensions whatever you want them to be. The most common dimensions for the board are 10 blocks wide by 20 blocks tall.
2. I do not want to comment on your method for storing the tetrominoes (game pieces). There is no standard way to store the blocks as they descend, it basically depends only on how you want to do it in order to make it work. Whichever method you find easiest is the correct method.
To find the starting shapes, and more information about Tetris in general, I recommend visiting
Tetris - Wikipedia, the free encyclopedia.