Both OneNote's will certainly be using the same Account (so you would need to use the same User Name and Password). They use your Microsoft account to sync into your OneDrive storage. The only time I know of Microsoft account prompting for a change of password would be if you forget your password or enter the wrong one in too many times. If you then change the password, it will change everywhere you are using your account.
There is only a single password for you account. There can't be multiple.
If this is not working your best bet is to speak to Microsoft. We can't do much to help you with account issues here.
Is your Outlook still syncing? It might have very well stopped when you where trying to log into OneNote, and the Contacts are no longer appearing. Best option would be to log into the Web interface for your email and check if the contacts are still there. If they are, you have a sync issue. If not, you can see if the mail account has a restore process. it's hard to say if it would or not without knowing the type of account it is.
There is only a single password for you account. There can't be multiple.
If this is not working your best bet is to speak to Microsoft. We can't do much to help you with account issues here.
Is your Outlook still syncing? It might have very well stopped when you where trying to log into OneNote, and the Contacts are no longer appearing. Best option would be to log into the Web interface for your email and check if the contacts are still there. If they are, you have a sync issue. If not, you can see if the mail account has a restore process. it's hard to say if it would or not without knowing the type of account it is.