Have there been mutations which have moved a species forward in evolution? If so, can it be proved?
Thats not really how evolution works. It's not that there was a mutation that moved anything forward. Evolution doesn't work like X-Men.
The way it actually happens is the world is constantly changing. The climate or environment changes or there is a disaster that strikes. Within a species there are constant mutations, and when these disasters strike or the climate or environment changes somehow, certain of the species around have mutated traits that enable them to survive these things better than the rest. The rest die out because they can't keep up.
The evidence for this is all around us. YOU are evidence.
its not that mutation pushes anyone ahead, rather its that it allows them to stay.