the collection of blue links in the sidebar on the left like "source(12)" are commonly referred to as the 'field picker'.
(Technically this is the 'MultiFieldViewer' module, and the 'FieldPicker' module is just the 'Pick fields' link and the associated modal popup layer).
The order of the blue links in the sidebar there is indeed always alphabetic. I dont think there's anything you can do to change that*. However when you click 'Pick Fields', and the big modal popup layer comes up, in the right side of that popup layer you can drag and drop the fields around to re-order them. However this will only reorder them in the EventsViewer module (where the fields appear just tucked under the event text), and in the SimpleResultsTable module (when you click the little table icon to view the events as a table instead)
*Well technically you could put some javascript into application.js that would augment MultiFieldViewer.getMatchingFields() so as to reorder them. But its not the sort of customization you'd be able to do on your own I'm afraid.
