A pair of parity puzzles

Create the above figure with 24 identical dominoes (or prove that this is impossible).  They may not overlap.

The above tetrominoes (as seen in Tetris) are sometimes called the O and N tetrominoes. There is a shape that can be built with four O tetrominoes OR with four N tetrominoes.  Is there a shape that can be built with an odd number of O tetrominoes OR with an odd number of N tetrominoes?  Find such a shape, or prove that it is impossible.  You may rotate and flip the tetrominoes, but they may not overlap.

If this sounds familiar, it's because I used a similar puzzle before.

There is a common theme with these two puzzles: parity.  Parity is the property of being odd or even.

See the solutions