The Salsa20 core function takes a 128-bit constant, 256-bit key, 64-bit counter, and 64-bit nonce and produces a 512-bit value. Or more generically, it is a mapping from 512-bit values to 512-bit values.
Is there a reason specific input bits were chosen for specific purposes? For example, if the some of the counter bit positions and key bit positions were swapped, would this result in a weaker cipher? What if we used the constant bits as additional key bits?
What about AES-Encrypt? If we view AES-128-Encrypt as a mapping from 256-bit values to 128-bit values, can we use whichever of the input bits we want for the key and
IV input block without weakening it?
Edit: Clarifying my AES question: I wrote IV but I meant input block. (Depending on the mode of operation, the input block might be an IV, plaintext block, counter, etc.)
And now that I think about it, it's clear that the key bits are different from the input block bits. Given the output of AES-Encrypt and the input block, it's difficult to determine the key. However, given the output of AES-Encrypt and the key, it's trivial to determine the input block: just apply AES-Decrypt.