How to add/delete columns to Symbol Editor Pin Table?
What kind of column do you want to add? Each column is a pin property. I’m not aware that additional pin properties can be defined.
You can right click on the header and that pops up a menu in which you can set visibility of the columns:
But overall. The amount and type of the properties are pretty much fixed. For what sort of pin information would you like to add a column?
On a side note. You can also see all the pin properties when you edit the properties of a pin. 
In the pin properties, there is also a section for Alternate Pin Function Definitions, and that is not visible in the pin table. I am not sure whether that is an omission (this function was added fairly recently) or by design (nested tables?)
(STM32 uC’s have these alternate pin modes defined).