How come there is only a start date when you create a task from outlook? Due date is greyed out.
You may want to contact the Support Team to see if they can troubleshoot what you're experiencing with the Outlook Add-In, but if you can post some screenshots (with any confidential information removed or blocked out) showing this behavior, I'll be happy to take a look at this.
It could be that you're linking to a sheet with Dependencies enabled. If this is the case and "Due Date" is used as an End Date in the sheet's Project Settings, entering in a "Start Date" and a "Duration" value should automatically populate the "Due Date". More information on working with dependency-enabled sheets can be found in the Help article titled Enable Dependencies and Use Predecessors
I hope this helps!