You should be able to use our Saved Search tool to make the list that you want. As for exporting only certain tasks, this is not currently possible, but you can export all your tasks and then import then into Excel to remove the tasks that you don't want.
I have always had a difficult time being able to pull up "Date completed." as a field, and can only locate it under Recently Completed. How can I do this via Search? Also, can I specify a date range in the search? Thanks.