Hi Siggy,
I don't know if this will help any, but from what I can see you're asking maybe a couple of different questions.
I noticed in your first post that you said your prime & your phone weren't recognizing each other, but then you don't go on to mention that again. Did that resolve?
As for watching live tv, if I understand you right, the "live" was the significant word there? Because there's Hulu Plus, Amazon, individual networks, etc for rebroadcasts. If your Prime is bluetoothed to your phone, which mine is (TF201 to Motorola Atrix on AT&T), & then you wifi hotspot your phone, then isn't there a way to watch live broadcasts? I would guess that then you'd have to find a site that's broadcasting it & I dont know, personally, of any that do that for free. I would guess that sites like Sports Illustrated will stream certain events live over the internet for a fee. I don't torrent or such as a matter of habit, so I don't know what's out there on all markets.
I connect my Prime to my Samsung SmartTV & Sony receiver & listen to playlists, browse photos & videos (SwipeIt is great for that, comes on the Samsung) via BubbleUPnP.
I've been really happy & lucky to have done some research & with luck & good sites such as this one, I've got things connected that I'm not sure are made to work with each other! Right now the puzzle we're trying to solve is getting our big tv to have Skype in the PIP & tv or the internet w/an external keyboard (without using the Xbox) on the rest of the screen. My husband & I like to Skype during the day, but I'd also like to be able to still watch tv or research, do internet banking, browse sites like this, etc, and the other two sources I have are this docked Prime in my Minisuit (all of which I have great fondness for) and the rest of the 52" plasma screen. If the Samsung SmartTv are going to do the Skype, we've got the camera for that, but it can't be in the PIP. I'm a very lucky lady & most problems are solved tech-wise, even with a spanking new tv & tablet (formerly a laptop).
Good luck,
Jennifer