Streaming iPlayer from MBP to AppleTV
Based on an article in 2012, it should be possibile to AirPlay this easily.
The quality will either be 720P or 1080P, buffering based on the quality of your internet connection. If your connection is fast you have no problems as long as your stream can handle it ;) 
Yes you can do this too, a cable is a direct connection not using Apple TV. It's cheaper as you don't have to buy an Apple TV. However, with Apple TV you can do much more - and it will show subtitles for example in a pre-chosen style.