First, the user should not be a domain admin as the normal user reading outlook and going to websites. It is a severe security breach.
This will prevent syncing other users's mailboxes if desired because the domain admin usually has been denied full access.
You could do it, but still not a great idea.
Next, make sure you specify that user has owner permissions to both the source and destination folder, even if the destination is the own users folder.
Right click, properties, permissions, add user as owner to both.
Next, it looks like SQL did not install. This happens with User Access Control still on, or the install was not run as an administrator.
Run MSConfig and turn off User Access Control in the Tools and REBOOT.
Then right click the full Add2Outlook full.msi and run as an administrator.
It should work then.
A question, I assume you are in Exchange hosted, and cannot use Add2Exchange to replicate, Correct? If you can use Add2Exchange, it is the best option if you can directly connect to Exchange and are not in hosted mode, or you are not replicating to PST files.