I'm a little confused about the 16A requirement for the power cable. Is this something that can be done at home with normal 3 prong US type outlets, or will I need an adapter/fuse/some other thing in order to use the S4?
If you're referring to a standard 15A 110V socket / circuit, then the S4 is not appropriate. 15A circuits are rating for 24/7 at just 12A. 12A @ 110V = 1,320W of power. 1,320W < 1,400W of the S4.
The cable requirement is just an additional requirement should you choose to ignore your circuit's rating (which you should not) in order for the cable to also not melt. Think of it this way - you'd think it weird if your microwave had the same cable thickness as your iPhone charger, right? Same sort of thing with the S4, its just bigger than most electronics in your house.