Do graphic cards have instruction sets of their own?

For nvidia cards you might want to have a look at this document http://docs.nvidia.com/cuda/cuda-binary-utilities/index.html#instruction-set-ref

Currently, NVIDIA cards use some kind of intermediate ISA called PTX. You can read about it in this document:

PTX ISA 1.1

PTX programs are translated at install time to the target hardware instruction set.

Yes they do. AMD even provides the specification up to the HD4000 series at the moment.

Take a look here at AMD's R700 instruction set reference guide.

There is also an open source project called Nouveau that does reverse engineering of the Nvidia instruction sets.

Note that Nvidia has a slightly different architecture than AMD because they do not use VLIW but scalar execution (although multiple threads are additionally grouped in what is called a Warp or a Wavefront).

Also, not every OpenGL/Direct3D call maps to a "GPU instruction". For example, when binding a texture the driver will only set appropriate hardware registers that tell the GPU which texture memory to use for sampling.

Real programs are only run when executing shaders or stream processing kernels on the GPU.

Yes, the GPU have their own proprietrary instruction sets. The GPU instructions are executed independent from the CPU instructions.