Well Gandalf is a maia also, so maybe that will clear things up for your brother. The Istari, or wizzards, were are all maiar, incarnated into the form of elderly men, and sent to Middle Earth by the Valar.

Did Glamdring (Gandalf's sword) survive the fall into the chasm at Moria? If it did, that could explain how Gandalf defeated the Balrog without his staff.

Wait, when talking to Aragorn, Legolas, and Gimli upon his return, he says: "Ever I hewed at him..." That would insinuate possesion of a sword, wouldn't it? I love it when I answer my own question.

Anyway, I used to be called Child of Eru around here, and now I'm back. Hi, everyone.

Welcome back! Have fun and post often

To my mind wizards's stuffs were more like part of their being (and they were, well, magical beings themselves) than some material objects. This can explain why Gandalf kept his stuff while being a prisoner of Saruman, who would have probably taken it away if it could be done. But this is what Frodo saw in his dream in Bombadil's house: So Gandalf escaped from Saruman with his stuff.

As for Gandalf's return after the battle with Balrog, he doesn't seem to have anything with him at all He was then carried to Lorien where he "was clothed in white". Maybe there, from elves, he also got the new stuff (or the material part of it)

Anyway, how exactly did the wizards use their stuffs? Well, for walking, as a common weapon, as a torch; but what about purely magical purposes? Were any actions performed with the stuff to make magic stronger? Nothing comes to my mind, though I didn't search.