The short answer is that any blockchain does not know what are your private keys only your public keys are known.
The long answer is that every time that you sign a transaction with your private keys it is only accepted by the blockchain (aka miners, block producers or witnesses) if it can pass a mathematical test by using your public key to verify that the transaction is authentic.
I do not understand how it works , still , I do accept that you guys get it and that's good enough for now.
Q: so the active key/private will still be the same for HIVE ? or just the public key?
All of the public keys are the same (essentially copied over). Since the public keys are the same, that means the same private key will work. The private keys are not on the chain; only you have them.
This applies to all keys (owner, active, posting, memo).
got it...almost ..
:)
They will both be the same. Although if you change your password after the fork they will be different after that point.
got it...almost ..
:)
If you're asking because you're worried - don't be. You will be able to log in and use apps/tools in exactly the same way as you do it now. Both public and private keys will remain the same.
Here you have a great article about keys: Steem Private and Public Keys Demystified
got it...almost ..
:)