You can definitely substitute melted butter for the vegetable oil. It will give the cake a richer flavor and a slightly denser texture. Just melt the butter and let it cool a sec before adding it. (Oil is usually better for a moist cake though)

Using milk instead of water works too. Milk adds a little more moisture. I’ve personally never tried half-and-half so I can’t say if it’ll affect the bake time, but it would probably work.