Thank you, ShagCA, for your well organized response. I have checked all the settings you mentioned above.
Incoming Mail Server: All are as you suggested except I can't find the SSL/TLS. In the Advanced section in "incoming settings" I see "IMAP Path Prefix / " and server port 993, but don't see "SSL/TLS: YES". (But these settings look exactly like on another iPad with iOS 10 which I own and AOL mail is working fine.)
Outgoing Mail Server: Everything is set as you suggested except:
The server port isn't 587...it's 465 (same as the other iPad in which AOL mail is working).
Instead of seeing SSL/TSL, I see "Use SSL" and the green toggle is turned on (but that section is grayed out and I can't make changes.
Hope you can make some sense of this. I am still perplexed. Thank you.