[2] In other words, modern encryption schemes are pseudorandom permutations and are designed to have ciphertext indistinguishability.
If an algorithm is found that can distinguish the output from random faster than a brute force search, then that is considered a break of the cipher.
[3] To prove that a cryptographic function is safe, it is often compared to a random oracle.
Classic examples of distinguishing attack on a popular stream cipher was by Itsik Mantin and Adi Shamir who showed that the 2nd output byte of RC4 was heavily biased toward zero.
[4] In another example, Souradyuti Paul and Bart Preneel of COSIC have shown that the XOR value of the 1st and 2nd outputs of RC4 is also non-uniform.