thanks for your question!
Hiding columns from view is possible by using a feature in the DataTables JS library (that is used for the sorting, search, and pagination).
Showing the hidden columns in a popup is non-trivial though, and I'm not sure what the best way would be to tackle that.
However, there's a similar solution that shows the extra data in an "expanded row". See http://www.datatables.net/examples/api/row_details.html for an example.
I don't have this ready either, but if you are interested, we could maybe work something out, so that I can develop this for you, if you compensate me for my time and effort. If that's the case, please send me an email, the address is in the main plugin file "tablepress.php".