It only needs the power adapter if your TV does not support MHL. If your TV is MHL compliant it will send power over the HDMI port and charge your phone. The standard is still new, almost no TVs support it yet. You can still mirror the screen over HDMI with a MHL adapter, but you have to power the adapter. MHL compliant TVs should be able to control the phone through the TV, but because those TVs are as common as unicorns I haven't tested it. With a non MHL compliant TV all it does is accept the input from your phone. You must still navigate on your phone. But, you can use a Bluetooth keyboard and/or mouse to control your phone wirelessly.
I got the cheapest MHL adapter on eBay that shipped free from inside the US. I think I paid ~$7. Its worked fine for me over the past 6 months.
Sent from my Galaxy S II (i777)