If you connect it via a HDMI cable and extend the screen from your Mac, the quality will be the lesser of either the maximum resolution of your graphics card in you Mac or the maximum resolution on your TV.
If you are planning on doing this on a regular basis, you can't go far wrong than having an Apple TV box. Allows you to rent and buy films, stream Netflix, stream music, films and TV from your iTunes account or your Mac (or any PC linked up to that network).
Great.
And the quality with the apple box would be that of the tv or the macbook to the same as above ( the worst one)
It runs either 1080p or 720p HD. You can link up any apple device to it via Airplay, so as long as you have a decent wifi network then shouldn't be a problem.
I stream HD films straight from iTunes, and I also Airplay BT Sport from my iPad to it (As I don't have Sky, but get BT Sport free with the broadband), and the quality has always been great.