I just use soap. Maybe degreaser (which is strong soap). I actually mix up a batch of strong soap water for the wheels, wheel well, and use it (and the same brushes) for the underhood work. Same brushes that get through the spokes, around the calipers, etc, are great for getting at the engine. Just use a hose, no pressure.

I wouldnt worry a bit about the alternator- its made to handle water.