Is prayer and fasting obligatory if blood is discharged during intercourse, followed by a brownish discharge two hours later, and nothing further is discharged, with four days remaining until the expected period?

This blood is not considered menses by the majority of scholars, because the minimum duration of menstruation according to them is one day and one night, unlike the Malikis. You both must continue to pray and fast until the bleeding returns and completes a day and a night to be considered menses. There is no sin or expiation upon you for intercourse as long as you were ignorant of this.