I had one or two connection drops the day I first used it, but never since then. It is automatically recognized as soon as you turn it on (I always turn the HS on when the console is fully booted now, maybe that helps)
You have to change the settings to hear people through the HS and not your TV. Normally, it should automatically go through your HS. On the XMB, go to settings > accessories > audio peripherals.
You'll be able to choose the output through your TV or HS. There's also a small bar on the top of the screen. Just try to speak and you'll see if it works
The bar will fill up. You can also set your mic volume accordingly. The default one (3 I think) should be fine, but just check it.