Frosting and darkening mean that the metal of the bore is no longer shiny - ie temporary surface corrosion or some other process has stained the metal. It can range from harmless discolouration right up to fairly bad pitting of the metal surface, and the effect on the bullet is also scalable - from no effect at all through to causing instability and poor accuracy. One way to assess a bore it to push a patch through - if it slides through reasonably smoothly, then the bore is probably just fine. If the patch feels rough, or snags up, then the pitting is bad enough to have effect on the bullet.
"Worn throat" happens to all barrels - its just the area of maximum wear in front of the chamber. Its particularly noticeable on old rifles with very worn barrels, especially those that have fired thousands of rounds of cordite. A bandly worn throat usually means the barrel needs to be replaced. Howver, if its a historic rifle with no spares available, then it just becomes a bit of a challenge to find an ammo/bullet type that will set up sufficiently to shoot accurately. Nearly ever rifle can still be made to shoot, no matter how badly worn the barrel...