Is the water that comes down with a light brown discharge, with a ten-day delay in menstruation, considered istihadah?

Brownish discharge (Kudra) is considered menses if it occurs during the usual period or is connected to blood. In this case, you should abstain from prayer and fasting. Otherwise, it is not considered menses; rather, you should perform ablution for prayer. If its discharge is continuous, then perform ablution for each prayer after its time has begun, and pray the obligatory and supererogatory prayers with that ablution until the time expires.