1. The GT610 is an older generation of card (I know the 6XX naming scheme makes that confusing). According to another thread on AVS, it does not support bitstreaming. It appears that you have to move up to the 640 to get bitstreaming capable cards. I'm not sure what the options are for AMD.
2. I don't know about the Raspberry Pi.
3. XBMC is really nice and since it is free and requires no codecs and minimal setup, you can give it a try without risking much.
4. I believe you can buy an inexpensive RC6 USB to IR adapter that will allow the Harmony to communicate with the HTPC. I too have tried the phone remote, and while it is nice, entering my phone's pin number each time I want to make a change is cumbersome. For this reason and the one you listed, I don't recommend using your phone as your primary control device.
5. I use an HDHomerun (digital channels only) connected to my network and Windows Media Center for my TV viewing. A lot of others really like the way WMC handles the guide and I see why. I have not gotten in to recording live TV, but it looks like that will work with the click of a button in WMC. I'm not sure how much there is in the way of configuring recording options since I haven't looked.