[Raynor]

True enough, the valar can make their own bodies as they see fit, according to the Annals of Aman:

Note that 'spouse' meant only an 'association'. The Valar had no bodies, but could assume shapes.

Of the istari, it is said specifically in Unfinished Tales:

Originally Posted by The Istari

For with the consent of Eru they sent members of their own high order, but clad in bodies of as of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die, and aged only by the cares and labours of many long years.

But again, what of Radagast? Could he change form? He was a master of "shapes and hues".

I don't think he constitutes an exception in that regard; if anything, he is lesser than Saruman and Gandalf. I believe his mastery involved what he could do to his environment/others, not unto himself; after all, Saruman has his voice while Gandalf wields the flame of Anor.

Edit:

Did he actually remember a time before he was "Gandalf"?

Yes he did; as Faramir recounts the words of Gandalf:

Originally Posted by The Window on the West, TTT

Olorin I was in my youth in the West that is forgotten

Olorin was his name as a maia in Valinor. Moreover, in Unfinished Tales, The Istari:

For it is said indeed that being embodied the Istari had needs to learn much anew by slow experience, and though they knew whence they came the memory of the Blessed Realm was to them a vision from afar off, for which (so long as they remained true to their mission) they yearned exceedingly.