The Speaker is a regular man, but with an abnormal connection to the Traveler that lets them kind of get dreams from it. The Light is a paracausal force (basically energy that doesn’t really obey the laws of reality) generated by the Traveler. It’s used for energy, power, Guardian healing, etc. It basically has infinite potential and some people have gone pretty crazy with it. Osiris can generate copies of himself. Kabr punched a hole through time and space to make a relic that could kill Atheon, the immortal embodiment of time itself. We can teleport short distances with it or conjure storms and vortexes of destructive power, make physical manifestations/projections of objects and weapons, etc. We still don’t know the possibilities of a Ghost choosing a new Guardian because of Bungie deliberately avoiding it and throwing out confusing/contradicting lore. Each Ghost has an ideal match for a Guardian (though they can choose to revive any unrevived person who has the Light) and once they revive their Guardian they are bound together. And yes, there are still cats and you can even see some in the Tower.