does a gsxr 600 k8 have any storage compartments? like under the seat or in the rear cowling?

l believe it has space under the seat for the tool kit

Yeah, under the rear cowl/seat you can fit a small bottle of water or soda can and snack bar. These bikes really have no usable storage space, you will want to use a back pack, tank bag or saddle bag if you hope to carry more then that. Now that the bikes have integrated signal lights there is even less room then in the past under the rear cowl, under the seat is the battery and ECU, no extra space.