What Can a Wizard Actually Do?

The thing about the Wizards—and pretty much any magical ability in Lord of the Rings in general—is that their powers are really, really vast, and really, really undefined. Even in physical form, as members of the Maiar all five Wizards had, to some degree, power over the elemental creation energies of the world itself, able to shape, create, and change it. Restricted as they were in using their full power by the Valar, the Wizards only resorted to some of their greatest magical abilities as a last resort, in an attempt to shield their true identities from the denizens of Middle-earth.
But even then, each Wizard was capable of incredible magical prowess. Channeled either through their staves or without, Wizards could do things like summon beacons of light, shoot mighty flames, telekinetically manipulate their foes, and use their magic to heal and bolster their allies. And although they had physical forms, their transformation into the Istari did not rob them of the essential immortality the Maiar had: as we saw with Gandalf when he perished defeating the Balrog, a felled Wizard would return to spiritual form and recuperate in Eru Ilúvatar’s seat, the Timeless Halls, before being reborn in physical form to continue their mission.