IS C2H available on the free web edition of Nios 2 12.1?

Judging by the names in those macros the hardware was generated by C2H. The C code used to generate the hardware accelerator can be somewhat confusing because that taps had to be written backwards to prevent the C2H compiler from optimizing everything away. If you are trying to look at the generated hardware files I wouldn't even bother, it's machine generated and it would be much quicker to look at a hand written implementation instead.

I don't know anything about that BeMicro design but I'm guessing the designer either used the old legacy tools that C2H supports, or they managed to use the legacy tools and then shoehorned the accelerator into a Qsys system and managed the accelerator manually. The latter is time consuming and very error prone so I don't recommend that anyone even attempt such a thing..... it would take too long to describe what can go wrong but from what I've seen others trying to do it normally doesn't work.