Yes, this only works with materials which are called insulators. Charges placed on the surfaces of such materials tend to migrate rather little, so a charged patch of surface will stay charged (for a while, anyway).
Among the choices you are given to select from, I incline toward (d). The problem with choice (c), if I'm understanding the intent of the wording correctly, is that the induced charging doesn't last. The example I gave of the charged rod and the foil-covered ball is what I think that is referring to. The ball is electrically neutral and is usually on an insulating tether (so the charge about to be applied doesn't just escape up the support) and the rod is brought close to it. The charge of the rod repels like charges in the foil to the far side of the ball and attracts opposite charges (actually, it's just the mobility electrons that move, but the effect is the same). This "induced charging" causes the ball to be attracted to the rod. But as soon as the ball touches the rod, it picks up some of the rod's charge and now has the same sign of charge as the rod, so it immediately jumps away from the rod.
The balloon obviously isn't doing that, so something else must be at work. That's why I think they are talking about the electric field of the charged balloon creating a polarization in the insulating material of the wall (in the same sense that a field polarizes the dielectric material in a capacitor), which produces a locally attracting region of the wall.