Is it permissible for a niqabi woman to pray in the mosque in her long clothes, to which some dust or water from the road may cling, and are these clothes considered pure for prayer?

The fundamental principle regarding objects is their purity, even if impurity is suspected. If you are certain of the presence of impurity, the default rule is that impurities are not purified except by pure water. However, because a woman's dress-hem is frequently exposed to impurities, dust has been made a purifier for it as a concession due to necessity, provided the impurity is dry. But if it is wet, it is more cautious to wash it with water.