S3TC is owned by HTC now. It's hard to know if they'll aggressively pursue users of this patent. HTC doesn't strike me as a particularly evil company, at least not on the scale of Oracle or Microsoft.
It's hard to know if the statistics reflect what's actually happening. For example, just ONE of the commits earlier this year pushed over 100,000 lines of code to get the ball rolling for HD7000 support -- which still isn't complete, but last I checked, you can successfully boot up a HD7000 in KMS mode, and use a 2D-only driver or llvmpipe to get working X.
No.
Yes, very heavily. Much of the grunt work of supporting recent AMD GPUs is thanks to Red Hat. They also help out Intel on their driver, they also work on old GPUs and server GPU chipsets for KMS support, and they also help with the overall architecture. Also, one of their employees, Dave Airlie, is the "chief" for the DRM (direct rendering manager) subsystem of the kernel, which basically means that he is one "rank" removed from Linus Torvalds in terms of decision-making power about what does or does not go into the Linux kernel's open source graphics drivers. Dave's task in that role is to take all the DRM-related patches, review them, and determine whether they are really ready for mainline. That way, ideally, Linus Torvalds never sees graphics code that's totally atrocious and untested and bad.
Oh, wait. Except that he does. Remember the "UNTESTED CRAP" fiasco?
Yes, the "etc" role is quite significant. Don't forget VMware, which is the company that bought up Tungsten Graphics. Tungsten is the company that originally designed the Gallium3d architecture, which is being used by all open source graphics drivers except for Intel's. The one guy who initially started the Mesa project way back in the 90s, Brian Paul, now works for VMware.
A lot of people who are either unaffiliated with a company, or working for some small business, are significant contributors to Mesa and/or the DRM stack. While a "majority" of the work may be done by large enterprises such as Intel, VMware and Red Hat, the individual / small business contributor is a huge part of Mesa.
I'm going to widen your question to include the entire open source graphics stack, which includes Xorg, libdrm, the DRM kernel subsystem, and Mesa.
In the approximate descending order by level of commitment (first one is most committed/best contributor IMHO): Red Hat, VMware, Intel, AMD, a few dedicated people who are unemployed or whose day job is unrelated to graphics drivers, Google, PathScale, Oracle, Apple, IBM, and a "long tail" of people from various companies and individuals who have between 1 and 10 commits (in other words, not a whole lot).