Hi Daniel,
I’d like to clarify these accounts:
Your first and third accounts are both Microsoft accounts, while the second one, the Office 365 account, is a Microsoft Online Services ID. Although you can use the same Office 365 email address to sign up a Microsoft account (your third account), the Microsoft account is different from the Office 365 account.
Currently, it is not available to use a Microsoft account to login to Office 365. Therefore, your first and second accounts could not be used to login to Office 365.
The credential which a Microsoft account uses will not take effect to the Office 365 accounts’. However, as you have two Microsoft accounts, in a browser, you would only be able to login one at a time. For example, if you have logged in with the first account, you would have to sign out to login with the third one.
Thanks,
Kevin Cui