NIOS I custom instructions

Yes. The 11-bit immediate is just the K register, which you set with a pfx in the assembly. I'm not sure how you would deal with that in C, and the only use for it I can think of is for some kind of 'mode' flag that makes the custom instruction hardware behave differently depending on its value. For passing arguments to your instruction (even if the arguments are compile-time constants) you're probably just better off using normal registers as you would with any other instruction. I think it is possible though, you could just have your C wrapper for the custom instruction do a PFX first with the argument you want to pass. There might even be a less hacky way of doing it if Altera has provided a suitable macro (SET_PFX_AND_DO_CUSTOM_n or something).