why every bitcoin public address have 2^96 private key and how can i find my (2^96- 1) private key for my bitcoin public address?
since Elliptical curve private key and public key has 1:1 ratio, and that public key is encoded & hashed with some operation to get bitcoin public address.
There are 2
256 private keys (actually just less than, but that is irrelevant to this discussion), 2
256 public keys, and 2
160 addresses.
As you say, private and public keys have a 1:1 ratio, but since to turn a public key in to an address you have to pass it through a RIPEMD-160 function, which only has 2
160 possible outputs, then there cannot be 1 public key per address. There are 2
256 inputs in to RIPEMD-160, but only 2
160 outputs, meaning that each output has 2
96 inputs.
also is it possible to encrypt message with bitcoin public address and then decrypt with private key which is generated by ECC.
It is possible to encrypt a message with a bitcoin public key and decrypt it with the associated private key, but not with the address. You need to either extract their public key from a transaction they have made, or ask them to share it with you directly.