The traditional angel food cake pan is a two-piece tube pan. A non-stick version will not work as that will hinder the cake from rising. The two pieces make it easier for removal and the tube shape helps the inside cook at the same rate as the exterior.
Yes, other pans will work, though they must not be greased nor should they be lined with parchment paper. The pan's natural surface allows the batter to adhere to the sides and assists with the rising. The timing must be adjusted, but loaf pans, sheet pans, jelly roll pans, etc. can be used.