How to find the secret key and nonce from two messages encrypted using the same nonce?
Short answer: No, the key and the nonce cannot be recovered from a ciphertext.

Longer answer with a big "but":  The encryption in  crypto_box is done using XSalsa20 which is a stream cipher.

All stream ciphers create a Key Stream $S$ and encryption of the message $M$ is then done using XOR addition: $C=M \oplus S$. Since the key steam only depends on the key and the nonce, you will get the same one in case of a nonce reuse.

From the properties of XOR follows, that I'd you add two ciphertexts, you'll end up with the XOR sum of the plain texts $C_1 \oplus C_2$. So if you know any plain text, you can easily recover every other message encrypted with the same key &amp; nonce combination.