The point of forward secrecy is that past key are not recoverable from future communications. You need to store the whole communication history to have any chance.
Unless you break the encryption. Then you get the past keys.
Forward secrecy only protects against the exposure of private key material. It does not protect against broken cryptography as it depends on the cryptography to keep old messages private. That's because it works by forgetting the session keys. If you can derive those session keys again then it is of no value.
Nope. A session key is normally not created by one party and sent to another, it's generated by something like Diffie-Hellman in which the long-living RSA keys are only used for authenticity verification.
Diffie-Hellman requires discrete logarithms rather than factorization (and then there are more modern methods).
Forward secrecy only protects against the exposure of private key material. It does not protect against broken cryptography as it depends on the cryptography to keep old messages private. That's because it works by forgetting the session keys. If you can derive those session keys again then it is of no value.