In regards to question #6, Cirdan gave up Narya so readily to Mithrandir because Cirdan being by far one of the wisest Elves ever to live, was the only one who knew at first who the Istari were, where they came from, and why they had been sent. Cirdan revealed this information to Elrond and Galadriel only. Here is a quote from page 365 where Cirdan gives Mithrandir Narya;
Gandalf was the closest in counsel with Elrond, and the Elves, and I think this fact along with Cirdan’s incredible powers of perception (since he was obviously aware of the tasks placed before Gandalf, and since he probably also perceived that something was amiss with Curunir) were the reasons that Cirdan entrusted the ring to Gandalf, and not to Saurman. One other thing I would like to add (and I realize this might be jumping the gun, but since I’m just starting to read UT for the first time, I’ll mention this as well) is a short quote from page 406 in Unfinished Tales;Take now this Ring, for thy labours and thy cares will be heavy, but in all it will support thee and defend thee from weariness. For this is The Ring of Fire, and herewith, maybe, thou shalt rekindle hearts to the valour of old in a world that grows chill.
But Cirdan from their first meeting at the Grey Havens divined in him the greatest spirit and the wisest; and he welcomed him with reverence, and he gave to his keeping the Third Ring, Narya the Red.
Galadriel I think wanted Gandalf to be the head of the White Council essentially for alot of the same reasons that Cirdan had entrusted Gandalf to the safekeeping of Narya. Again, it was because Gandalf was the closest in council with Elrond and the rest of the Elves, because he was the most vigilant, and because I believe that Galadriel being as powerful as she was, also perceived that Gandalf was the greater and wiser spirit, and that he had been sent with the higher purpose. I also think it very likely that after a while, she also perceived that something was amiss with Saurman, although due to his power, he did a good job of hiding his true intentions even from the wisest for a long time.