Why use IV like this in TLS 1.2 record layer AES-SHA block cipher?
I am curious why do we use IV like that. Why not derive IV in the key expansion and use it again again?


Repeating IVs is bad, both for CBC and GCM.  And, no, keeping the repeated IV secret from the adversary doesn't help.


  If we use it like above, the IV will be public to anybody.


Well, yes.  IVs do not need to be secret; we don't mind if an adversary hears them.


  Is it right that the recipient should use the IV to decode block-ciphered struct?


Yes.  In CBC mode, the IV is directly used as the CBC-mode IV input (effectively, as the "previous ciphertext block" to decrypt the first ciphertext block).  In GCM mode, it is combined with 4 bytes from the key expansion to generate a 12 byte nonce, which is used as the GCM-mode nonce input.