I don’t think their DNA has been sequenced, but I’m willing to bet someone made babies with Homo floresiensis. I think bestiality must be a no-babies thing. As far as I’m concerned Homo floresiensis is blurry memory elves. Maybe weak, but I plug my no vote.

That’s how you get Bretons

Although often considered a slur nowadays, Half-elves were the most common interspecies offspring in D&D.

It would only be considered beastiality by racists that view elves (or more likely, the humans) as animals.

Yes, first quoting Sir Terry Pratchett:

J.R.R. Tolkien has become a sort of mountain, appearing in all subsequent fantasy in the way that Mt. Fuji appears so often in Japanese prints. Sometimes it’s big and up close. Sometimes it’s a shape on the horizon. Sometimes it’s not there at all, which means that the artist either has made a deliberate decision against the mountain, which is interesting in itself, or is in fact standing on Mt. Fuji.

As such let’s look at the Granddaddy of all modern Medieval Fantasy, in Tolkien’s work there are several human/elf couples of renown, from Beren and Luthien which are not in the movies so people don’t usually know to Aaragorn and Arwen (who are a central point of the movies). Not only that, but we know that they can produce offspring, because Elrond is a half-elf, not only is he a half-elf, but both his parents were half-elves.

In short, yes, they do.

Falka did in The Witcher, at least.