Only local variables are eligible of residing in registers (see also Declaring Variables in a CUDA kernel). You don't have direct control on which variables (scalar or static array) will reside in registers. The compiler will make it's own choices, striving for performance with respected to register sparing.
Register usage can be limited using the maxrregcount options of nvcc compiler.
You can also put most small 1D, 2D arrays in shared memory or, if accessing to constant data, put this content into constant memory (which is cached very close to register as L1 cache content).
Another way of reducing register usage when dealing with compute bound kernels in CUDA is to process data in stages, using multiple global kernel functions calls and storing intermediate results into global memory. Each kernel will use far less registers so that more active threads per SM will be able to hide load/store data movements. This technique, in combination with a proper usage of streams and asynchronous data transfers is very successful most of the time.
Regarding the use of device function, I'm not sure, but I guess registers's content of the calling function will be moved/stored into local memory (L1 cache or so), in the same way as register spilling occurs when using too many local variables (see CUDA Programming Guide -> Device Memory Accesses -> Local Memory). This operation will free up some registers for the called device function. After the device function is completed, their local variables exist no more, and registers can be now used again by the caller function and filled with the previously saved content.
Keep in mind that small device functions defined in the same source code of the global kernel could be inlined by the compiler for performance reasons: when this happen, the resulting kernel will in general require more registers.
