I know spome folks will insist on honey mustard sauce, but these are Balrog wings we’re talking about here! It’s got to be spicy barbeque, if you ask me. I think I’ve got a recipe around here somewhere…
The reason you don’t see many elf kids is that they take only a few years to grow up (not more than a hundred or so), but after that, they can live for tens of thousands of years. So statistically, there aren’t very many of them. But if you want to see elf children, there are plenty of them in the framing story for The Book of Lost Tales.
As for birthday spankings, as I recall, elves usually reckon time in longer units of (I believe) 144 years. And they don’t celebrate birthdays anyway, but conception days, but the elven gestation period is just about a year, anyway, so it works out to about the same thing.
Much though I fear to disagree the great Mercotan, I’m not convinced that reborn elves are confined to Valinor. The only case we know of is Glorfindel, who was in Middle Earth both before and after he died. (For you non-obsessed fans, he was the elf who helped chase the Wringwraiths at the Fords. In his previous life, he went mano a maio with a Balrog, and died taking it with him.) And I’m also not too sure about Arwen’s choice. She says that she chooses a mortal life, but is that really her choice to make? Recall that she does not die of old age (she’s still in her prime when Aragorn dies, and mortals don’t get much longer lived than Aragorn), but rather of grief, one of the two causes of death to which Elves are subject. I think that only Elrond, Elros, Earendil, and Elwing were given the Choice.
While it’s technically correct to say that humans and elves can interbreed (it’s happened at least three times), those were probably the exceptions rather than the rule. There are other accounts of humans and elves marrying, but (with the possible exception of the house of Dol Amroth’s supposed Elvish ancestry) those unions didn’t result in any children.
And re Aragorn’s elven blood: Aragorn and Arwen are first cousins, 43 times removed. Elrond’s brother Elros was the first of the kings of Numenor, the land of Aragorn’s ancestors. Strictly speaking, Elrond and Elros weren’t half-and-half, either: They (and all their decendants, like Aragorn) also have some divine blood on their mother’s side, from Melian the Maia, who married the elf Thingol.