Thanks, everyone, for the PhD-related lauding. I appreciate it!
As for Crook (and maybe that's an unfortunate name, but it came to me one day and it stuck), I appreciate all of your advice and the links you provided!
Crook has fathered no babies, and I don't intend to allow him to breed.
debbie276, no, his beak is not crossed, as far as I can tell. His brother has no malformation. Nor do/did his father and mother (the latter now deceased). The other juvies of Cucumber (joint father to Crook, his as-yet-unnamed brother, and two as-of-yet-unspecified gender mothered by Currant, the sister of Crook's deceased mother) also show no beak issues. (By the way, I know these family relationships sound confusing, but there has been no inbreeding, unless it happened with Currant and Clover before I owned them.)
Also, of course, I am keeping him. He has rather endeared himself to me: he seems to be the most personable/least afraid of me of all my finches, and when I come close to the cage he usually pops over to "say hello." When I whistle at him, he sings for me. How could I not love that

? I mainly just want to make sure a) he is not in pain, and b) this is not a life-threatening medical issue that needs to be addressed. Since it has been present from the beginning (and he is about 6 months old now, maybe closer to 7), I am inclined to think it is a mutation rather than a disease/virus/infection etc.
I know his beak is not looking so hot, but I think he will turn out to be a very pretty bird in terms of coloring. He is showing signs of a fine orange mask, I think. This has sentimental value to me because his mother Clover, my only OH hen, passed away from a wing injury shortly after her babies fledged. So, at the risk of sounding sappy, I see his mother in him. sniff.
This is going to make me sound inexcusably ignorant for someone who has owned finches for over a year (in my defense, I have never had to deal with beak issues before), but does it cause a bird pain to get his beak trimmed? Is it, say, more like a person or a dog getting his/her nails trimmed (i.e. painless), or like a cat getting declawed (basically the opposite of painless)? I'm not planning on trimming his beak myself, but I would like a better understanding of the process.
It doesn't come through in these photos, but I am wondering if he will be lilac-breasted? His dad is WB, mom PB. His adult breast plumage looks much lighter than that of his brother (who, by the way, is looking like he is going to take after his father with a red mask).
Thanks again for your input!
(ps his "aunt" Currant is totally photobombing those pics!)