this has nothing to do with NatTable. The context menu you are seeing when performing a right-click on the text in a TextEditor is the default context menu for the org.eclipse.swt.widgets.Text class. As far as I know you can not add items there. But maybe you can change it.
I'm not sure what you mean. In fact there is already a hotkey to enable editing of a cell (press F2 to open the cell editor of the current focused cell).
If you want to add some custom functionality on an open cell editor, you have to search on how to do this in the org.eclipse.swt.widgets.Text widget. The open cell editor is an eclipse text editor and not specific to NatTable.