Well... your responses:
a) Can Indian nationals drive in spain with their indian licenses?
NO. You need an international driving license. Check
DGT (in spanish), the official spanish traffic authority for further explanations.
b) Is it better to own a car or is the best way to travel by metro / bus?
Madrid is a mad city for drivers. Everyone drives quite fast and agresively. I have a driving license but avoid driving in Madrid. In fact I haven't a car. Underground and bus networks are extensive and effective within the city limits. If you live far in the metropolitan area or you need to travel often to other cities, a car is needed. Otherwise: NO.
c) Are there any monthly passes that one could buy for metro / bus travel? How much?
There are monthly passes, they have different costs depending on the zone around Madrid that you are going to. The farther, the more pricey.
The zones are coded A, B1, B2...
Approx cost for A is 30 EUR .
Abono mensual de transportes de Madrid