Do contacts and calendars come too?

Not over the app password. Export them as .vcf and .ics files at AOL, then import them on the Contacts page and in Calendars.

The import paused. What now?

AOL stopped accepting the app password. Make a new one and choose Enter a new password on the import, and it carries on where it stopped.

No. Imported mail is not run through your rules, forwarded or announced, and running it twice adds nothing.

Migrate from AOL Mail

Make an app password at AOL and your mailbox is copied here, folder by folder. The old mailbox is only read, never changed.

01
Make an app password
At login.aol.com/account/security, choose Generate app password, name it Nextmail and copy it.
02
Choose its address
Add your domain here, or pick an address you already have. The mail is filed under it.
03
Start the import
Open Migrations, choose From a mailbox, enter the old address and paste the password. Check the mailbox, then start. You can close the page while it runs.
04
Keep your address
Connect your AOL address in Addresses, and its new mail arrives here with the rest. Replies go out through AOL, from the same address.

A workspace takes a minute. Add your domain, then copy the old mailbox.