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Can my private key be generated when someone else creates a wallet? If each private key is generated completely randomly, then I think my key can be generated repeatedly I created a wallet, but on etherchain.org "First seen" = never, this means that someone else will create this wallet and not know that it was created by me

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If the random 256-bit number is really random and it was generated in a secure way, the chances of someone else guessing it is so low that we could say it's impossible in our life span.

Something to note is that an Ethereum address is the last 20 bytes of the keccak256 hash of the public key.

So, in theory, if someone creates a private key that generates a public key whose, at least, the last 20 bytes of its keccak256 hash is the same as an existent address, yep, someone else would have the same Ethereum address as you. But still, 20 bytes is 160 bits, and the chances of repeatedly creating random private keys and creating public keys from them and passing them to keccak256 to return a hash whose last 20 bytes are the expected 20 bytes are really low. A 160-bit number is still huge.

But back to your questions. If you create an address and you don't do anything with it, you don't use it ever, you don't send balances to it, etc., and randomly a person in the future generates a random private key that generates a public key whose last 20 bytes of its keccak256 hash are the same as the address you generated before, there's no way that person could know that that address was already generated by someone else before. But again, chances are that nobody will generate that same address ever.

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