A) You receive 10 payments to 10 different addresses, and spend 5 of those payments, then subsequently change your password. Would you still be able to spend the 5 unspent inputs? If so, with what mechanism?
B) You receive 10 payments to 10 different addresses, and spend all 10 of those payments, then subsequently change your password. Subsequent to changing your password, you receive an additional payment to a previously used address. Would you still be able to spend that input? If so with what mechanism?
For both of the above, you would still be able to spend the Bitcoin. The previously derived and used private keys and their related transactions remains in the wallet file. Unlike some other wallets, and much like most wallets, Bitcoin Core does not generate the private keys on the fly, it generates them and then stores the private keys and all related transactions. Those previously derived and used private keys are kept. However, the master private key is deleted (IIRC), or at the very least, no longer used, once the password has changed.
C) You calculate 10 addresses that are associated with your xprivkey, but do not do anything to let Core know that you have given these addresses out (eg you never click on "receive" -- or whatever it is called), and change your password. You subsequently receive bitcoin to those 10 addresses. Would you be able to spend those 10 inputs? If so under what mechanism?
I don't think you actually would be able to spend those 10 inputs because Core does not keep keys that it has not marked as used. However, they might actually be spendable from Core because Core should still be tracking transactions related to those addresses. I will have to look at the code.
Edit: It looks like those inputs would be spendable because checking whether a transaction is part of the wallet does not care whether the addresses is used or not.
I guess my broader question is what happens to your xprivkey when you change your wallet password with Core?
The extended master private key is deleted, or at the very least, no longer used. The previously derived and used private keys remain in the wallet as well as their related transactions.