1~~~ change email for your Adobe ID
If you have any old DRM books authorized to the ID, you want to keep the same ID.
If you aren't expecting any information sent to your email, you can just continue using the old email address.
The fact that it doesn't work any more doesn't matter.
It might be worth changing to the new email, for example if you forget your Adobe password.
If you want the email address up to date, change the email address associated with the ID.
To do that, log on (sign in) at the top right of www.adobe.com, using your old email address.
Go to 'My Adobe', 'My Adobe ID' (https://www.adobe.com/uk/account/account-information.html#myadobeid)
Change the Adobe ID in the top right and save the changes.
That does not change the underlying ID and your rights to read associated books,
but changes the email address associated with the ID.
Devices already authorized to the underlying ID may continue to show the old email address,
or they may at some random time notice the change and show the new email address.
Don't worry, it is the underlying ID that matters, not the email address.
One ADE2.0, you can see the underlying ID by menu/Help/Authorization Information;
that will show both the underlying Adobe ID (urn:uuid) and the email it thinks is associated.
2~~~ authorizing second ereader.
Plug it in when ADE is running, and in ADE2.- menu/Help/Authorize Device (on the superior old ADE1.7.2, menu/Library/Authorize Device)