1. I'm going to have a stab at using Vonage with LinuxMCE over the next few weeks, so I'll let you know how I get on if you're still interested.
2. Thin clients, yes, pretty much anything, provided it can do a network (PXE) boot. Another hurdle is the graphics - if you're wanting to use the high end UI, then you'll need nVidia, or VIA UniChrome I believe, not sure about drivers for that though.
I've been looking at building my own thin clients using a mini-ITX motherboard. Having sourced the motherboard that I want to use (1 Ghz fanless processor, VIA Unichrome grpahics, S-video, DVI, gigbit LAN), along with the power supply etc, I intend on building my own case for it (due to the high cost/unavailablity/large dimensions of other thin mini-ITX cases that I have seen) which should end up around 1.5 - 1.75 inches thick. Not quite as good as the 1" Fiire ones, but remember this - I intend on mounting my computer to the wall, behind the TV, not on the VESA mount itself. This means that with a swing arm-type TV mount, I will actually be able to get the TV closer to the wall than would be possible with the 1" client. And for a much lower price.
For smaller TVs (where it really IS necessary to have the PC sandwiched between the TV and the VESA mount), I intend on building a custom all-in-one TV bracket and mini-ITX computer case. Ideally I want the PC and/or case to be removeable, but this may mean sacrificing how close you can get the TV to the wall. Not sure what I am going to do yet, but that's the fun of design. I'm working on the CAD for this now.