How old is Dumbledore's phoenix, Fawkes?
My motivation is mostly curiosity, but also because I believe the age might tell us something interesting about Dumbledore.
If Dumbledore adopted Fawkes when the bird was young, then perhaps Fawkes chose Dumbledore because it was raised by him. Or perhaps it had not lived long enough to know many humans and accepted one of the first humans to care for it.
But if Fawkes is of immense age (centuries or millennia old), then it has encountered hundreds or even thousands of humans over its many years. For Fawkes to choose one particular human, Dumbledore, among all those it met means that Dumbledore was truly someone special to it.
Garrick Ollivander, the wand-maker, uses their tail feathers to make wands. Ollivander prefers to use only three animals for wandmaking: unicorn hairs, dragon heartstrings, and phoenix feathers. One might think phoenixes were somewhat common for their feathers to be used for such a common tool. Yet, to my best knowledge, none of the Harry Potter stories even mentions anybody else owning another phoenix, or even mentions a phoenix besides Fawkes.