#2
I don't think there are any families missing from the Manual of Nearctic Diptera, but some of them appear as subfamilies - particularly within the Tipulidae, Mycetophilidae and Empididae. If you want alternative keys, then Oosterbroek's key to European families has most, though not all, of the Nearctic families. For initial sorting, I'd be tempted to stick with the old (inclusive) families in any case.
#3
I agree with Tony Irwin's comment. There is no single better source to identify adult insects to family.
Some other references:
Merritt and Cummins, An Introduction to the Aquatic Insects of North America. This has the only key I have seen to fly pupae. It only covers aquatic families, but terrestrial families are mainly indistinguishable (as pupae) Cyclorrhapha.
Manual of Central America Diptera. This book uses alternate methods to key out Nematocera and Oestroidea, and separates the Central American families of Mycetophilidae sensu lato.
Soli's key to Palaearctic fungus gnats will be useful, but note that
Paleoplatyura will end in the wrong family because it has an r-m crossvein.