That's exactly where I see folk have issues.
Remember we are dealing with -> Windows <- and while I prefer to use Bluetooth A2DP I can't write a tutorial or more here. For that we turn to the internet, google and more.
After you've done this a few times you begin to think "what were they thinking?" as you find you didn't repeat the same steps with each setup.
-> Apple and it's AirPlay is a lot better and a bit less wonky.
About amplifiers. Since the common BT Audio receiver can't drive a speaker (I use them with headphones) that's a pretty easy question. Yes.