There's no functionality like this built-in to the grid.I'm not sure where these symbols come from. Do they exist as normal characters or are they perhaps using Wingdings or some other special font?
If they are part of every font, then this would be a simply matter of creating the dialog and adding that character into the text of the cell.
If they come from a special font, then you would have to change the Style of the cell to FormattedText so that you could insert a font tag and specify a font for a character or range of characters.
This should help:
HOWTO:What is the best way to place a DropDown list in a grid cell?
I don't think there are any events that fire when you click on an item in the list specifically. But I'm not sure I understand exactly what you want to do.
Maybe you can use the CellListCloseUp event on the grid? This event will fire when the list closes for whatever reason.