Does frequent movement, such as moving one's nose to stop a runny nose or adjusting one's garment away from the place of prostration, invalidate the prayer, and are these movements considered minor such that they do not harm the prayer?

Slight movements, such as raising one's nose or pushing one's garment, do not invalidate the prayer. Such movements may be a result of waswasah (whisperings/obsessive thoughts), in which case one must ignore and disregard these whisperings.