You can tell if a amplifier uses the ground just by looking at the back of the product itself. I have several amps and AV products which drop the ground.
The way you KNOW this is by looking at where you connect the power cord. There will only be the hot and the neutral pins, there won't be the third pin on the actual product for a ground connection.
While it may seem weird to still use an IEC plug even though there is not a ground pin, this is entirely because of the common form factor of the IEC cord. You can pick them up EVERYWHERE and after you buy a computer or two, you often end up with spare IEC cords stored away in a bin somewhere.
There is absolutely no harm in using a 3 pin IEC power cord with 2-pin gear, because it won't have a pin to make that ground connection.
You also won't be able to fit the 2-pin IEC power cord into a 3-pin product. This is because on the end of the IEC cord, it is filled in and solid where there is normally a hole for the ground connection. So, the ground pin will block that cord from going into equipment which needs the ground.
To your other question: The Home Depot 14AWG speaker wire will work just fine for you. If you want something nicer at some point, you can go on the hunt for something you like more, but really, it won't perform any better.
THIS:
I guess wire is just wire.
This is the mantra which Audioholics subscribes to. For the most part, wire of the same gauge will perform the same as long as the material is the same. Just pick the right one, and you are good to go.