PIC is not a single architecture. PIC10 differs considerably from PIC24, though they and every PIC in between share some commonality. The MIPS based PIC32 on the other hand is an entirely different architecture. So you have to be clear about what PIC you are referring to.
An OS on a PIC does not have to be and RTOS, but that would be ideally suited to the application domain the devices are used in, so anything that were not real-time capable would be somewhat less useful.
There are many RTOS ports already for PIC.
There is nothing special about about a kernel scheduler in terms of development method, C and in most cases a little assembler are all that are necessary - no special tools. You could use 100% assembler if you wished, and this might be necessary to get the smallest/fastest code, but only if your assembler knowledge is better than the compiler's.
PIC is specific to Microchip, though Parallax SX is more or less a clone. Unlike ARM for example, Microchip do not licence the architecture to third-party chip manufacturers or IP providers. No one would want it in any case IMO; there are far better architectures. ARM Cortex-M is particularly suited to RTOS kernel implementation, and AVR's instruction is designed for efficient translation from C source code. Even the venerable 8051 is well suited to RTOS implementation; its eight register banks make context switches very fast (for up to eight threads), and like ARM, 8051 architecture devices are available from multiple manufacturers.