>>Thank you very much for your message.
>>First, Exchange back end is out of the question. I don't have the skill and the resource for it.
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>The main issue is you would need a different e-mail address, such as one on outlook.com. Otherwise, the difficulty level in getting set up is similar to Gmail.
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>>I will need to figure out what my iPhone and iPad use for connecting to the Gmail server. It is not clear if it is POP3 or IMAP.
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>I believe iOS defaults to trying IMAP and using it if available. But if you set it up a long time ago, or set it up manually it might be POP3.
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>>In the Outlook, I will need to move the message(s) from the .ost file to a .pst file (where I have folders for different purpose). This way, I will not rely on the .ost file. And having email messages in a .pst file will provide a good storage.
>>Does the above make sense?
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>Don't get fixated on the ephemeral .ost cache file. You don't move items from there to a .pst, you're moving items from the Gmail server to a local .pst file. You probably don't want to do that - if an item is removed from the Gmail server, it will disappear from other devices once they sync.
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>If instead you copy items from Gmail to your local .pst, they will still remain at Gmail and be visible on your other devices.

On the iPad I see that the emails are set to use IMAP. And before today the Outlook used POP3. That is, different devices were using different protocols and it worked. Now I will have to set all, Outlook and iOS devices, to use IMAP.
The reason I move my emails to a local .PST file is that I have many folders in the .PST file and store email messages in different folders. Depending on the purpose. That is, the messages in .PST file are categorized. This has been working for me for years.
But I don't understand why you are saying that "You probably don't want to do that." Once an email - item is in the local PST file, I have it. No?

UPDATE.
>>You probably don't want to do that - if an item is removed from the Gmail server, it will disappear from other devices once they sync.
I routinely delete email messages from my iPhone/iPad. Now, since Outlook will get these messages from the server via IMAP, the messages will be deleted from the server and my Outlook. This will be a problem since I will lose the message completely. This is why I want to copy or move a message from the Outlook .ost file to a local .pst file. This way, the message is not lost.