To be perfectly honest, I don't know why it wouldn't work in a 10 or 11 FJC. I'm not sure if the spot on the dash is still there or not? Maybe they changed the wiring harness and it's no longer equipped with the plug for it? Not really sure though. I know that Toyota says 2007-2009 for it though and I verified that with Tech Assist this morning.
As far as compatibility with the subwoofer, I don't know why it wouldn't work. As far as I can tell, it really doesn't have anything to do with the factory sub in any way. I'm looking at the installation instructions right now and it doesn't mention anything at all about interferences of any sort.
According to the installation instructions, this is indeed a plug and play installation.
Thanks for posting that picture. However, if you use Google Images and google the part number, PT917-35071, it shows pictures of the nav unit. In your post, you noted the part number as having a -WH on the end which would indeed be JUST the harness.