Is the Salsa20/ChaCha20 keystream generation one-way? Is it possible to recompute the Salsa20 or ChaCha20 key in a realistic time if the keystream and the nonce are given to an attacker? Or is the keystream generation one-way, like a cryptographic hash function?
Nobody should be able to retrieve the key from the IV + key stream. If that would be possible then the stream cipher would be broken. Both the IV and key stream can be considered public knowledge (by performing a known plaintext attack, for instance using all zero's). Retrieving the key from information that may be known to an attacker constitutes the strongest attack possible, so any stream or block cipher should protect against that situation.

Or, as fgrieu already states without making it an answer:


  A keystream generation algorithm which key, assumed unknown and uniformly random, can realistically be found from the output keystream and input other than key, is broken by definition of key per Kerckhoffs's principles, and/or of the security objectives of a keystream generator/CSPRNG.