Does opening of ion channels alter the membrane potential directly? Does the opening of a voltage-gated ion channel (i.e. the change of configuration of the protein) by an appropriate local change of the membrane potential directly and significantly alter the membrane potential in turn? Like the influx of ions that was caused by the opening of the channel does directly alter the local membrane potential? (Assume there were no ions going through the channel: would there nevertheless be a significant change of the membrane potential by the mere opening of the channel?)

Not in any substantial way from the perspective of the overall membrane potential; it could be possible to measure the charge moving as a way to study channel gating, but that's a completely separate issue (and the scale of measurement would have to be incredibly precise, way more precise than is relevant for neural function).

Although very few ions have to move across the membrane to change the membrane potential, this "very few" is in relationship to the total number of ions present in a solution, which is massive and difficult to imagine. A single ion channel can flux millions of ions per second.