Distribution kernel-header packages contain, as their name implies, only kernel header files (plus the necessary plumbing) that are required to build software like kernel modules.
You shouldn't expect to find binary files at all in a kernel source directory, except for build output. (If you configure and build a kernel yourself, the kernel source directory will also contain the compiled objects, modules, the built kernel itself and a few other binary bits and pieces that make it work.)
KConfig files are a description of the kernel configuration options (and their dependencies) that are available for a given directory/module.
Apart from that, it's all (mostly) C source code, header files and Makefiles. There are a few helper scripts here and there, and assembly source too.
Header packages only contain the header part of the above (and not all of that - only the "exported" headers), and some of the build infrastructure. So what you are seeing is expected.
On Ubuntu, if you want the full kernel sources, I believe you should install the linux-kernel-devel package. (See here if you want to build a kernel yourself.)
/usr/src/linux is a traditional place to put kernel sources, but nothing prevents you from putting kernel sources elsewhere. This path is also often just a symbolic link to a directory. e.g. I have this on my machine:
$ ls -l /usr/src/linux
lrwxrwxrwx 1 root root 18 Dec 7 17:03 /usr/src/linux -> linux-3.1.4-gentoo
The symlink is there to simplify building applications that depend on the kernel source. You link that path to your running (or target) kernel so that you don't have to specify exact version or path information when you build a module out-of-tree. Helps a bunch for source-based distributions at least.