What is the ruling regarding the prayers of my mother who used to wipe over socks that covered from mid-foot to the knee, believing it to be permissible, so are her prayers during that period valid?

A condition for wiping over leather socks (khuff) or regular socks (jawrab) is that the sock must cover the obligatory area [for ablution]. The sock mentioned in the question does not fall under the ruling of wiping over khuff because it does not cover the obligatory area. If removing the medical sock harms the patient or delays their recovery, then its ruling is that of a splint (jabirah): one wipes over its entirety, from top and bottom, and the rest of the exposed foot is washed. As for making up the prayers that were performed in that state, some scholars are of the opinion that making them up is obligatory, while others believe it is not. If this is difficult for her, or if the period was long, she is excused due to her ignorance, and there is no need for her to repeat them, according to the more sound of the two opinions of the scholars.