I'll chime i here.
1) Gaming was my very top concern when I first started my home theater. I use XBox 360, and a custom top end i7 PC. I like to mostly play COD MW2 and Black Ops online. I was looking for something that handled motion as well as possible, and since I game online, also something with the lowest input lag so that I'm not at a disadvantage against other players online. From the "input lag of various projectors" thread, I learned that the Infocus IN83 had the least measured input lag, practically nill, and handled motion as good as it gets. After I got the IN83, the all the other positives of it are what really got me into movies as well.
I jumped on the SP8602 as soon as it came out, of course I paid a lot more then than you would now, but it was well worth it. My only concern with the upgrade was of course input lag, and it does have slightly more lag, but I can tell you that it's definitely not enough to have any affect on my gaming ability. Over time my stats remain unaffected, and motion is flawless.
I now use frame interpolation for movies, although I didn't like it at first. Frame interpolation adds an amount of input lag that I believe would affect competitive gaming, based upon some crude testing I'd done outside of gaming, but I can leave frame interpolation on all the time with having to worry about it. This is because games are at 60Hz and frame interpolation isn't being processed, while it is for my movies, so it works out very well for me.
2) I use Windows 7 dual monitor configuration, where you can specify 1920x1080 for the projector, and separate resolution for the monitor. However, I also use a 1920x1080 monitor so that the pixel "real estate" are the same. In the office, 1920x1200 has some advantage, but no advantage over 1920x1080 in the home theater.
3) No. Of course that's my view. Infocus has their projectors under warranty repaired by an outside service. The major components are still available and should be for a long time. I know because I asked this when I had mine repaired. However, I've read here at least a few instances in which Infocus had given upgrades to newer projectors when older projectors could not be fixed.