Is the Linux kernel affected by paging? Is the whole kernel always loaded to RAM whatever the size of the RAM? In other words, can the Linux kernel be affected by paging (some part of kernel reside in virtual memory)?

No, (at least not that I am aware of any feature allowing for the kernel to load in swap) it makes use of the paging system (or swap) for LKM's and running processes.

The linux kernel is loaded into system memory. Depending on the size of the kernel (which would grow exponentially when used without loadable kernel modules, or static modules for device drivers etc.) the system may/or may not have enough physical memory to load. It then exposes an API for both 'kernel' & 'user' land memory resources. Here is a resource for ARM chipsets.