Is there a relationship between the content of a private RSA key (private exponent, modulus and primes) and a AES-128-cbs key and iv?
I know that you can encrypt your private key using AES in which case the AES-iv is supplied in the pem file and the AES-key is calculated using MD5 over secret-password and the first 8 bytes of the AES-iv.
However I have AES encrypted data and a private RSA key that I can read. Is there a standard on how to derive the AES-key and AES-iv from the RSA key content, maybe from the prime numbers inside. Is there some standard that is normally used?
No, it makes no sense to have your symmetric key depending on your asymmetric.
Usually you also don't just encrypt one particular AES key with one RSA keypair. Instead what you usually want to do is to use for example someone's public key to encrypt a randomly generated AES key and send the RSA encrypted key along with the AES encrypted data to the recipient. This way you can use a different symmetric key for every data package.
This is just one use case, but it illustrates why there is no reason for such a dependency.