Is it permissible for the questioner's mother to use blood pressure medication brought by a relative who works in a government hospital, without knowing whether he obtained it with permission or not, and what is the ruling on what she has consumed of it, and how can one repent if there is any wrongdoing?

There is no sin upon your mother in accepting the medicine and benefiting from it, as long as she does not know, or it is not highly probable in her estimation, that your relative transgressed concerning the medicine. The basic principle is that a Muslim's wealth is his property. If the man is known to have unlawful wealth, then dealing with him is abandoned as a matter of piety. As for the Muslim whose situation is not known (mastoor), there is no doubt in dealing with him in the first place.