How to solve this decryption algorithm given the encryption algorithm?
Here's a hint about the second part of the question:

b. Is the given system perfectly secure? Prove your answer.

Hint: what is the encryption of the plaintext $(0, 0, 0, 0)$?  If the ciphertext is something other than $(0, 0, 0, 0)$, what can we infer about the plaintext about that?