Is the method of washing ritually impure clothes by pouring water and soap on them and washing them alone correct, and does the water remaining ritually pure mean that its color or smell has not changed after washing? And if this method is incorrect, does that mean that everything I have washed previously is not ritually pure?

First, to purify defiled garments, water should be poured over them to remove the impurity. If a defiled garment is placed in a small amount of water, the water becomes defiled. As for the water that separates from the garment after the impurity has been removed: if it separates altered (by the impurity), it is impure; otherwise, it is pure. So, if water is poured over the impurity and its trace is completely removed, or if the place is submerged, if the impurity was hukmiyyah (legal/non-sensory), until its removal is highly probable, the garment becomes pure. However, if the water separates altered by the impurity, the place has not become pure, and it must be washed again until the water separates unaltered.