What is the ruling on disconnected or intermittent brown discharge, and is it menstruation that prohibits prayer or not?

This brownish discharge you observed is not considered menses due to its lack of connection to blood and its occurrence outside the time of your usual period. As long as you are not certain of having seen blood, the default assumption is that you have not seen it. What you did, in terms of praying and continuing to observe the rulings for ritually pure women, is correct. The minimum duration of menstruation, according to the majority of scholars, is one day and one night, so this droplet is not considered menses.