[Raynor]

Originally Posted by Legate of Amon Lanc

Nevertheless, Melian, I believe, had her "Valinorean" form on her (cf. below) when she met Elwë

I doubt she retained her cloak-like body after felling in love with Thingol. In Myths Transformed, it is said:

Originally Posted by Orcs

...by practising when embodied procreation they would (cf. Melian) [become] more and more earthbound, unable to return to spirit-state (even demon-form), until released by death (killing), and they would dwindle in force.

However, more to the point:

Originally Posted by Of the ruin of Doriath, Silmarillion

For Melian was of the divine race of the Valar, and she was a Maia of great power and wisdom; but for love of Elwe Singollo she took upon herself the form of the Elder Children of Iluvatar, and in that union she became bound by the chain and trammels of the flesh of Arda.

Originally Posted by Legate of Amon Lanc

I'd also like to see what happened when he returned at the end of the Third Age: if he kept his form of Gandalf the White, or changed into something else (Olórin the Gray, Olórin the White...).

I don't think he had any reason to keep his embodied, severely limiting form, other than sentimental reasons