I have run into a problem with adding new email addresses to the same
contact. After adding the name, I tab to the next field, and the address
disappears. I cannot get it to save.

Also, how do I clear out all the email addresses that pop up when I begin
typing in a name or address in the 'To:' field of a new email?

Frustrated wrote:

I have run into a problem with adding new email addresses to the same
contact. After adding the name, I tab to the next field, and the
address disappears. I cannot get it to save.

Also, how do I clear out all the email addresses that pop up when I
begin typing in a name or address in the 'To:' field of a new email?

With Outlook closed, delete the (hidden) file
$AppData%\Microsoft\Outlook\{profilename}.NK2. That will remove ALL the
cached autocompletion data. If you want to remove only a particular entry,
when the list pops up, use the down-arrow to select the name you don't want
and press Delete.
--
Brian Tillman