Do feet movements to remove the edge of a skirt stuck to them during Ruku' invalidate the prayer, knowing that this occurs in every Ruku', and that it can be avoided before the prayer? What is the ruling on adding other necessary movements to that?

Moving the foot away from the edge of the garment, and other similar minor actions that the worshiper needs or is compelled to do, do not invalidate the prayer and there is no harm in them. The Prophet, peace and blessings be upon him, used to pray while carrying Umamah bint Zaynab; when he prostrated, he would put her down, and when he stood up, he would pick her up.