Yes, if you got the exact same address, then you would have one of the 7.9 X 1028 (on average) working private keys for that address.
That is correct. There are 2256 private keys with 2256 public keys. The public key is hashed with ripemd160(sha256(pubkey)). Ripemd160 is limited to 2160 possible solutions thus[1] there are 2160 possible addresses with 2256 private keys or 2256/2160 = 296 private keys per address. 296 ~7.9*1028
[1] under some minor assumptions like even distribution
Basically you have a better chance of winning the lottery AND being hit by lightning than guessing the correct private key for a given address. As pointed about in a prior post, the math can change drastically if a faulty RNG was used.