Short answers, pulled from the story.
Gruiformes means "crane form." The order takes its name from the large cranes that are among its most recognizable members, though the group also includes rails, crakes, trumpeters, limpkins, finfoots, and many other bird families.
The traditional order Gruiformes was established by Max Fürbringer, a German avian comparative anatomist, in 1888. He grouped together bird families that did not seem to belong to any other order based on comparative anatomy.
No. Modern molecular studies have shown decisively that the traditionally recognized Gruiformes consist of between five and seven unrelated clades. Only the core Gruiformes - the suborder Grues, including cranes, rails, limpkin, and trumpeters - represent a genuine natural group.
The Australian plains-wanderer (Pedionomidae) and the button-quails (Turnicidae) were moved to the shorebird order Charadriiformes. The kagu and sunbittern now form the proposed new order Eurypygiformes. Seriemas and bustards represent distinct unrelated lineages, and several fossil families once assigned here belong instead to the order Cariamiformes.
The core Gruiformes, grouped in the suborder Grues, include rails (Rallidae), flufftails (Sarothruridae), finfoots and sungrebe (Heliornithidae), adzebills (Aptornithidae), trumpeters (Psophiidae), the limpkin (Aramidae), and cranes (Gruidae). These are the only families considered true Gruiformes.
Houde and colleagues in 1997 were the first to present molecular genetic evidence of gruiform polyphyly, using 12S ribosomal DNA sequences. Later work by Fain and Houde in 2004, Ericson and colleagues in 2006, and Hackett and colleagues in 2008 confirmed the finding decisively.