Is it obligatory to make up the Shafa and Witr prayers after purification from menstruation if their time has passed due to the onset of menstruation? And is there a sin incurred by that? And is it permissible to use prayer beads (tasbih) during menstruation?

There is no sin upon the questioner for leaving what is not obligatory, nor is she to be blamed for delaying the Witr and Shafa' prayers. Their time begins after the 'Isha' prayer and extends until dawn breaks. Since she was prevented from performing them due to an excuse, she is not religiously required to make them up after purification. A menstruating woman may worship and remember Allah Almighty through all forms of remembrance, except for prayer and what is similar to it.