Is the kernel stack for all process shared or there is a seperate kernel stack for each process? If it is seperate for each process where is this stack pointer stored? In task_s
There is just one common kernel memory. In it each process has it's own task_struct + kernel stack (by default 8K).
In a context switch the old stack pointer is saved somewhere and the actual stack pointer is made to point to the top of the stack (or bottom depending on the hardware architecture) of the new process which is going to run.