Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Perhaps my best bet would be to find a 3rd party mail program that could coordinate these accounts with a central data base for contacts, and stop fighting Outlook? Do you have an ideas for that?
I have really appreciated your help.
Honestly, not sure what you mean by that. No email client stores contacts in a central location - it's all governed by how (POP3, Imap, Exchange) those connect to the email accounts.
The fact that you have an Outlook.com account, your contact/calendar info contained in the Outlook.com contact/calendar folders would be accessible by all devices when the account is added (configured) to the device including your Android phone.
As for data files in Outlook
For Outlook '2010 and later (ergo - all Outlook versions)
POP3 accounts are stored in a PST file with contact/calendar data being local to the device where the account is configured
For Outlook '2010
IMAP accounts use 2 PST files - one for email folders which are sync'd with the server and another for contact/calendar folders which like POP3 are local to the device
For Outlook '2013 and later
IMAP accounts use an .OST file which sync's with the server for email folders. Contact/calendar folders have the words "This Computer Only" in the the folder description and local to the computer where the account is configured
Outlook.com accounts
If configured as an Exchange or IMAP account - it uses an .OST data file.
Can be configured as either POP3, IMAP or Exchange (the default). If configured as POP3 or IMAP, contact/calendar data is not sync'd with the server. Not a limitation of any email client whether Outlook or otherwise, it's an industry standard definition of the protocol.
Store your contact/calendar data in an Outlook.com account folders and the data will be accessible by all devices connecting to the email account as long as Exchange (Exchange ActiveSync) is used as the protocol. The only other thing that you would need to ensure is to set the Outlook.com data file as the "default data file" in Outlook desktop (any version). To do that, go to File --> Account Settings --> Data Files tab --> select the Outlook.com .ost data file and set it as the default.
You might want to start with answering a more basic question given the information above "What problems exactly are you encountering"? (Don't think upgrading to Office 365 is going to resolve anything that you can't deal with in '2010 so first order of business would be to address the problem(s))