Analysis looks sound to me, using msg content to derive the key is generally bad form, especially messages are known to attackers and sent repeatedly. (eg. Hi)

It looks like a bunch of convoluted code that doesn't actually accomplish anything.

Why is

  sha1_a = SHA1 (msg_key + substr (auth_key, x, 32));
  sha1_b = SHA1 (substr (auth_key, 32+x, 16) + msg_key +   substr (auth_key, 48+x, 16));
  sha1_с = SHA1 (substr (auth_key, 64+x, 32) + msg_key);
  sha1_d = SHA1 (msg_key + substr (auth_key, 96+x, 32));
  aes_key = substr (sha1_a, 0, 8) + substr (sha1_b, 8, 12) +   substr (sha1_c, 4, 12);
  aes_iv = substr (sha1_a, 8, 12) + substr (sha1_b, 0, 8) +   substr (sha1_c, 16, 4) + substr (sha1_d, 0, 8);

better than

  sha1_a = SHA1 (msg_key + auth_key);
  sha1_b = SHA1 (sha1_a);
  sha1_с = SHA1 (sha1_b);
  sha1_d = SHA1 (sha1_C);
  aes_key = SHA1(sha1_a+sha1_b+sha1_c);
  aes_iv = SHA1(aes_key+sha1_d);

and more importantly why is it better than

  aes_key = RANDOM
  aes_iv = RANDOM

Are there special properties of the random bits of parts of various hashes that makes it more 'random'?

To me it looks like repeatedly sending the same message, or a message whose hash varied by a few bits, would leak part of the auth key, basically the person probably doesn't know what they are doing and are just adding extra 'stuff' to assure themselves it's secure.

The comments from TFA doesn't say a shit but full of "you are wrong, because you don't understand it" without debating the technical details.