No because Gwaihir arrived expecting to give information to both Saruman the White and Gandalf the Grey. What was that Gwaihir said..."Why find I Gandalf alone on this perilous height, and why speak you of traitors?"...I don't have a copy of LOTR handly to confirm, of course.

: 2)When Elrond's messengers went to find Radagast at Rhosgobel and he wasn't, where was he? Had he moved? Was he still on his way home from Eriador? Could he have been conversing with Gwaihir?

Dunno, I believe he may have, unlikely and maybe. In that order. I think it very likely that Radagast MAY have been forced to leave due to the dark presence in Dol Guldur. MAYbe. Raddy was after all an Istari and could have held his own against any of the Nazgul, and then some. But against the might of a fortress that was obviosuly attempting to take control of the area, hence the attacks on Lorien, I think he may have had to retreat. Maybe to Lorien itself, though that's never mentioned so maybe not, and maybe to Northern Mirkwood, to join up with Thranduil.

Who knows...

Cheers

Padster