In The Silmarillion, we get the story of Melian and Thingol; Melian, being a Maia, does not have a body that she is bound to, but rather was able to take on the shape and likeness of creatures of the world or the children of Iluvatar.
But...she bore a child. Lúthien Tinúviel, who was never described as being anything other than a (particularly beautiful) elf. This, as The Silmarillion might phrase it, is a thing strange to me; that a being using a body the way we use clothing could be capable of bringing forth one of the children of Iluvatar. The Maiar, after all, are not supposed to be able to create new life, yet that's very much what motherhood is. So...
Is there any indication in the text or letters or similar that Melian was 'incarnated' the way the Istari were? Was Lúthien a 'child by adoption' of Eru, as the dwarves were?