DirectX programming in C?

You can use DirectX in C. It has specific macros to simplify the use of the COM interface. However, it's much easier to use C++.

The Open Watcom C/C++ compiler comes with DirectX sample applications in both C++ and C. Both work. They are under WATCOM\samples\directx\cpp and WATCOM\samples\directx\c respectively in OW 1.9.

This is what the code looks like in C++:

hr = d3d->GetDeviceCaps(D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, &d3dcaps9);
hr = d3d->GetAdapterDisplayMode(D3DADAPTER_DEFAULT, &d3ddm);
hr = d3d->CreateDevice(D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, game_window, D3DCREATE_HARDWARE_VERTEXPROCESSING | D3DCREATE_MULTITHREADED, &d3dpp, &d3d_dev);

And in C:

hr = IDirect3D9_GetDeviceCaps(d3d, D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, &d3dcaps9);
hr = IDirect3D9_GetAdapterDisplayMode(d3d, D3DADAPTER_DEFAULT, &d3ddm);
hr = IDirect3D9_CreateDevice(d3d, D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, game_window, D3DCREATE_HARDWARE_VERTEXPROCESSING | D3DCREATE_MULTITHREADED, &d3dpp, &d3d_dev);

You don't need to do anything special with COM in C as there seem to be enough macros defined that you can just use.

Yes it is possible. DirectX exposes a COM interface and C is capable of consuming them. It won't be a whole boat load of fun though!