I'm about to move to mumbai so is the water safe to drink, brush my teeth, and shower in?

Not the best. Several websites confirm the poor water quality in mumbai, especially during the monsoon season when water supplies are contaminated even worse. Travelers are advised to drink only bottled water (inexpensive, but make certain the seal is intact) & use only bottled water for brushing teeth. Avoid ice cubes & salads that may have been made with tap water.
Travel. Allow 4-6 week before traveling to prepare for trip. During that time review immunizations required for country you are going to. Read cdc.Gov and read travel recommendations : it covers vaccination, travel diarrhea, malaria, etc and give so many suggestions. Buen viaje.