Is it permissible for my wife to pray, and is it permissible for me to have intercourse with her if her menstruation stopped, then the blood returned intermittently after a few days?

If the wife sees the well-known signs of purity, then bleeding resumes:

- If it is after fifteen days, then it is a new menstrual period, and she should refrain [from prayer, etc.] for the duration of her usual period.

- If it is before the completion of fifteen days, then it is irregular bleeding (dam fasad) which does not prevent prayer, fasting, or sexual intercourse. This is most likely what occurs with your mentioned wife.

- However, if the blood intermits during the known period of habit, then there is a difference of opinion among scholars regarding this issue.