How do we get the OWA Web Part to work without prompting you to add user credentials and to autodetect the user without prompting for a password?
Hmmm…Interesting. 
The best workaround I have seen for this so far is to set up x2 web sites on your OWA server. One web site can be configured with FBA [Forms Basic Authentication] or Basic Authentication [mail.yourcompany.com] which is used for primary OWA use within your organization and the other web site [spmail.yourcompany.com] is configured with Windows Authentication which is used for just SharePoint web part usage.
Using the windows authentication site [spmail.yourcompany.com] within your web part will automatically log the user onto the OWA server without re-prompting for the password.
Makes sense when you think about it. 
bobbyhabib