The Kindle app for your computer is to actually read Kindle books. It doesn't talk to a real Kindle at all and actually appears as a whole extra device in your Kindle management page. You don't need it.
All the USB port is used for is to transfer files as it appears a standard USB mass storage device and to charge it. You can charge it from any decent USB charger or from a computer. You don't specifically need the Amazon charger but if you do want to use it then you can use it anywhere in the world with a plug adapter as it is capable of working from 110V or 220V.