You need to pick the Create Date on the Closure object, ie the date that the closure was created, and the Analyst that closed it will be the CreatedBy value. As its the Close object, I'd also expect the Create values to be the same as the Last Updated
I was able to find the Create Date on the Closure object and tried to drag it into the "Selected Attributes" section however it keeps going into the Preview at the bottom. I want this column to be seen on my finished query but it shows up as a Preview on the bottom and contains no data. Why am I not able to add this as a column heading like the others I have selected?
That would be because your query is based on Incidents, and the Closure Object is a collection - when you drag the attribute from the collection it drops it in the preview pane. You need to start your query on the Closure object, and if you need any attributes from the incident you can get to them through the relationship.
Hope that makes sense!