Is the new iphone capable of using a MHL cable to connect to HD TVs?

On the other hand, it would appear in fact yes: http://www.crutchfield.com/S-hpbGFJIbabC/p_530HDMI5/Soundstream-HDM-i5-Cable.htm l

I'm told that Apple's Lightning Digital AV Adaptor in fact compresses the video … the link above is to a product which /claims/ not to do so. Disclaimer: I don't have first hand experience of either!

You use a standard HDMI cable and an adaptor like this:

http://store.apple.com/us/product/MD826ZM/A/lightning-digital-av-adapter?fnode=4 5

No.