Skunks hunt at night, sometimes around dusk or dawn as well, but usually go back to their den around dawn. They mostly eat the eggs and will go after chicks or small chickens. Members of the weasel family also will eat the heads, but typically they kill a bunch of chickens. Always remember...
I'm not BearFoot, but yes, a hawk is a raptor. The only sure way to keep a hawk out of the run is to cover it. I have a much smaller run (about 200 sq ft) and I used deer netting for the top. I believe I spent a little under $30 for a 7' X 100' roll and some zip ties that I used to 'connect'...