Proving that there is no scheme which would be perfectly CPA-secure
The perfect indistinguishably under a chosen-plaintext attack: Pr[PrivK_cpa = 1] = 1/2
Is my argumentation correct to this point?

No, because the question doesn't ask about 'perfect indistinguishability' (which would include computationally unbounded adversaries), just indistinguishability against probabilistic polytime adversaries.
Assuming that the adversary has access to the public key, then here is an adversary that achieves an advantage $&gt; 1/2$:

Select a set of random coins; send them through the $Gen$ function

Compare the public key generated with the public key presented

If they are the same, use the private key generated to decrypt the ciphertext and use the resulting plaintext to make the decision.

If they are not the same, select a random bit and use that as the output.


Now, if this procedure selects a set of random coins that just happen to be the same as the coins used during the original key generation process, then this always achieves the correct answer (or, at least, with high probability if the public key system has a small probability of decryption failure); if it does not, then this gives the correct answer with probability at least 1/2 (&quot;at least&quot; because there may be other sets of random coins that result in the same public key; those would also give the correct answer).
Hence, if $\lambda$ random coins were used in the key generation process, this gives the correct answer with probability $2^{-\lambda} + 0.5(1 - 2^{-\lambda}) &gt; 1/2$