We know that Maiar can and often do take humanoid forms, or perhaps sometimes elvish forms. Sauron did this while he still could (1st and 2nd ages); the Istari did it; Luthien’s mother Melian presumably did so too.
What is our understanding of how their Maiar powers affect them while they are in humanoid form? Do they have their full powers (if they are not otherwise constrained, like the Istari were mostly)? If their offspring get some benefit from their Maia-ness, like Luthien did if I’m not mistaken, how is that passed (i.e. is there any mechanism or explanation other than “magic”)? When they assume humanoid form, do they imbue their forms with some analog of DNA, that includes Maia qualities and that can be passed on?
Finally, would there be any difference whether the father vs. the mother were Maia, and whether the other parent were elf vs. human?
I will be surprised if Tolkien actually dealt with any of the mechanics of reproduction among the exalted, but it did happen, so do we know anything about it?
(Perhaps this is part of the question about how the Maiar mate with each other – do they have to assume physical bodies to do so? And a host of other similar questions that spring to mind. But I’m most interested in the inter-being matchups.)
So far as I know, Melian is the one and only known example of an Ainu reproducing. As for the how, remember that the Ainur were the ones who created the World in its physical form: I suspect that Luthien was a special act of creation, and that Melian and Thingol sang her into existence, much like, long ago, Melian and her colleagues sang the World into existence. Which probably did involve her physical form going through the same processes as mortals do when we mate, but may not have involved “DNA” or “angel genes” or the like.
Well, if she was the only one I suppose that makes it a special case and there is no general answer.
I wonder if she had to get any sort of permission, from the Valar say, to take that step of reproducing, no matter how she actually did it.
Originally the Valar were going to have offspring but along the way Tolkien dumped that idea. Eönwë the Banner-bearer of Manwë started as the child of Manwë & Varda.
In fact, Oromë was originally the child of Aulë and Yavanna.
If there was any special “permission” involved, it would have been from Illuvatar Himself, not from the mere Valar. But of course, He tends to communicate subtly: It wouldn’t have been a matter of her saying “Hey, 'sup, Big Guy, Thingol and I would totally like to do the horizontal tango and make a little rugrat, 'scool with you?” and Him replying “Sure, go for it, have fun”. More likely, she knew in her heart that it was right, because of her love for Thingol.