Can I use Redstone underwater?

Nope, you can't place them on tiles with water, they pop back up. If you have placed them already and water flows over them then they will do the same.

Bonus edit:

Here's a picture of me trying to place a redstone torch down, while a sheep looks on in bewilderment:


Yes, if you make a tunnel. Here's some images of me doing just this: enter image description hereenter image description hereenter image description here