In general you can choose global_work_size as big as you want, while local_work_size is constraint by the underlying device/hardware, so all query results will tell you the possible dimensions for local_work_size instead of the global_work_size. the only constraint for the global_work_size is that it must be a multiple of the local_work_size (for each dimension).
The work group sizes specifiy the sizes of the workgroups so if CL_DEVICE_MAX_WORK_ITEM_SIZES is 512, 512, 64 that means that means your local_work_size can't be bigger then 512 for the x and y dimension and 64 for the z dimension.
However there is also a constraint on the local group size depending on the kernel. This is expressed through CL_KERNEL_WORK_GROUP_SIZE. Your cumulative workgoupsize (as in the product of all dimensions, e.g. 256 if you have a localsize of 16, 16, 1) must not be greater then that number. This is due to the limited hardware resources to be devided between the threads (from your query results I assume you are programming on a nvidia gpu, so the amount of local memory and registers used by a thread will limit the number of threads which can be executed in parallel).
CL_DEVICE_MAX_WORK_GROUP_SIZE defines the maximum size of a work group in the same manner as CL_KERNEL_WORK_GROUP_SIZE, but specific to the device instead the kernel (and it should be a a scalar value aka 512).
You can choose not to specify local_work_group_size, in which case the opencl implementation will choose a local work group size for you (so its not a guarantee that it uses only one workgroup). However it's generally not advisiable, since you don't know how your work is divided into workgroups and furthermore it's not guaranteed that the workgroupsize chosen will be optimal.
However you should note that using only one workgroup is generally not a good idea performancewise (and why use opencl if performance is not a concern). In general a workgroup has to execute on one compute unit, while most devices will have more then one (modern CPUs have 2 or more, one for each core, while modern CPUs can have up to 20). Furthermore even the one Compute Unit on which your workgroup executes might not be fully used, since several workgroup can execute on one compute unit in an SMT style. To use NVIDIA GPUs optimally you need 768/1024/1536 threads (depending on the generation, meaning G80/GT200/GF100) executing on one compute unit, and while I don't know the numbers for amd right now, they are in the same magnitude, so it's good to have more then one workgroup. Furhermore for gpus it's typically advisable to have workgroups which at least 64 threads (and a number of threads divisible by 32/64 (nvidia/amd) per workgroup), because otherwise you will again have reduced performance (32/64 is the minimum granuaty for execution on gpus, so if you have less items in a workgroup, it will still execute as 32/64 threads, but discard the results from unused threads).