*flexes the corded muscles of concentrated nerd*
Galadriel was born in Valinor, a long time after Elves awoke at Cuivienen, and was indeed around in the time of the trees, though if I recall she is the youngest of her family. She came to Middle Earth with Feanor in the first age (about 4000 years before the War of the Rings). However, the Age of the Trees in which she was born reportedly lasted tens of thousands of years, so she is old indeed. She really never demonstrates any combat potential whatsoever. Her power lies mainly in foresight and wisdom, as well as leadership. She can apparantly block the Eye of Sauron as he tries constantly to spy within Lorien, which is no mean feat.
Also, Gandalf the Grey is certainly powerful, but is pressed to hold off even a portion of the Nazgul at Weathertop. He is forced to leave before meeting Strider and the hobbits there or else risk facing them all (and their dread captain). If Gandalf could take the Witch-King before his rebirth, he doesn't show it, and indeed seems to actively avoid a confrontation with him. At any rate, anyone who doubts what the Witch-King can do should look up the scene with Grond at the gate of Minas Tirith. Gandalf the Grey can't match that (but it adds weight to Gandalf the White standing in the aftermath).
Also, equating Gandalf to a Balrog would be inaccurate. Gandalf is not (to my knowledge) a spirit of fire, specifically. His power over fire comes by his own admission from special studies regarding the subject, and is likely augmented by the Elvish Ring of Fire, which Cirdan gave him. His magical abilities more often reflect light and lightning than fire. When he refers to himself as a "Servant of the Secret Fire", I think he is talking about the Imperishable Flame of Illuvatar (Pretty much God), which is what allows the creation of life. Spirits in Middle-Earth change form according to their natures. Morgoth was once a princely being, and eventually lost his ability to take this form as he commited more and more acts of evil. The Balrogs are hulking, superpowered fire-demons because of how their actions have shaped them.
A note on Bombadil relating to all this talk of age: When asked about his origins, he replies: ""Eldest, that's what I am." And that he "remembers the dark when it was fearless, before the dark lord came from outside". He was in Middle Earth before Morgoth was, and this puts him in the uncounted years before even the Age of the Lamps. Tom Bombadil is almost certainly the most powerful being (as age often equates to power in Lord of the Rings) to ever exist in Middle Earth, possibly exempting (some of) the Valar themselves.
Just don't you tread on his lilies.