A "sequential memory-hard" PoW scheme cannot be parallelized effectively thus I imagine you also can't distribute solving the puzzle between participants in a pool? How does that work with scrypt then - for instance how do litecoin mining pools work?

Correct me if I am wrong, but equihash is "just" memory-hard. I understand you are solving a generalized birthday problem among randomly generated bitstrings. But my question here is: how does the pool verify you are actually doing meaningful work. Like with a "traditional" PoW you submit partial solutions that don't match the network difficulty but still have some difficulty "attached" that prove you did some work.

For equihash I believe there is no "partial" solution, either you find the inputs that xor to zero or you don't. What am I missing?

Are there any zcash mining pools out there yet? How do they ensure "fairness"?