What is the ruling on Fajr prayer and what follows it, and is it obligatory to abandon prayer with the presence of brown discharge, or a small amount of blood that does not continue, and is not accompanied by the usual symptoms of menstruation?

This brownish discharge is not menstruation as long as it does not occur during the usual period and is not connected to blood. And this slight bleeding you saw is not considered menstruation according to the majority of scholars, because the minimum duration of menstruation for them is one day and one night. Therefore, your prayers are valid, and you are not considered to be menstruating until you see blood and its flow continues, along with any yellowish or brownish discharge connected to it, for a period of one day and one night.