No, Mumbai is usually considered as a part of western India. Here's a map for your reference: Source. As you can see, Mumbai is right at the western edge. There is literally just the Arabian sea after Mumbai in the west. read more
i think i can answer this, as i have livd in mumbai for 7 years. 1. mumbai is not a state , its a metropolitan city of india. 2. yes , it is on souther side of india but not actually south. rest read here to know more about mumbai. read more