Some papers that may, or may not, answer your first question (I have yet to read them fully, but I'll get round to it in time) are the following:
On The Osteology And Phylogenetic Affinities Of The Pseudasturidae – Lower Eocene Stem-Group Representatives Of Parrots (Aves, Psittaciformes) by Gerald Mayr,
Zoological Journal of the Linnaean Society,
136: 715-729 (2002) [Full paper downloadable from
here]
A New Psittaciform Bird From The London Clay (Lower Eocene) Of England by Gareth H. Dyke & Joanne H. Cooper,
Palaeontology,
43(2): 271-285 (2000) [Full paper downloadable from
here]
Comments On The Systematic Position Of The Putative Lower Eocene Parrot Pulchrapollia gracilis by Gerald Mayr,
Palaeobiodiversity and Palaeoenvironments,
81(2): 339-341 (2001) [Full paper downloadable from
here]
Two New Parrots (Psittaciformes) From The Lower Eocene Fur Formation Of Denmark by Dvid m. Waterhouse, Bent E. K. Lindow, Nikita V. Zelenkov & Gareth J. Dyke,
Palaeontology,
51(3): 575-582 (2008) [Full paper downloadable from
here]
One answer that I can provide with respect to parrots, is probably the same answer that applies to the diversity of life on coral reefs among the brilliantly coloured fishes living in those biotopes. Namely, that species recognition is an important issue in an environment where you have numerous closely related species. Bear in mind additionally that many of these birds inhabit rainforests, and frequently, despite their lavish plumage, they're not
that easy to see amidst dense foliage. Third, amongst the rainforest foliage, you'll also find lavishly coloured flowers, and in an environment where the green of the rainforest is punctuated by these flowers, having brilliant plumage isn't necessarily a disadvantage. Fourth, if you've ever tried to catch a parrot that doesn't want to be caught, you'll quickly learn that they're not easy prey at all - they're accomplished fliers, and are also equipped with beaks that can inflict some very nasty injuries upon the unwary, particularly amongst the cockatoos and larger macaws. A Hyacinthine Macaw, for example, has a beak that has evolved over time to give the bird the ability to crack open Brazil Nuts, and a beak that can deliver this sort of bite force is going to be an excellent defensive weapon. In the case of cockatoos, they're more than willing to use them, as I've found out the hard way with a particularly aggressive specimen from a local pet shop a few years back. Even a budgerigar can deliver a nasty nip if it is so inclined, and remember, parrots frequently use their beaks to excavate holes in tropical hardwoods for nesting purposes, so they're well equipped to bite back if something tries it on with them.
However, when you have something like 200 species of parrot sharing the same biotope, it's essential that they mate with the right partners. Consequently, males and females have an interest in being recognisably individuals of the 'correct' species, so to speak, and for organisms with acute vision, coloured plumage is the obvious option, just as coloured body patterns are the obvious option for coral reef fishes possessing the requisite colour vision to discriminate between the patterns.
You might also find
this Google Books link useful.
