I can understand your situation since I come as well from a country where parents convince their offspring to join either: medicine, engineering or pharmacy. Because they think these are the "secure" jobs. Although the following might sound intuitive to many readers, I expect that people coming from developing countries (like me) might find this advice valuable.
Your parents speak out of their experience from what they see around them. I would assume that, like in my country, it is true that mathematicians do not have many good opportunities in India.
So to answer question (1), I assume that in India this is true. In other countries that might not be the case, although it is true that in general medical doctors will probably earn more than mathematicians, but in many countries (e.g. western European countries) you (as well as your family) can live a very decent life with a mathematician's salary.
(2) As others said already, mathematicians can get jobs in research, IT and as well in insurance companies.
Now my advice is to do what you love and let it eat you! this will sound Utopian to some, but no it is true, you can do what you love and live a decent life a the same time, you do not have to do something you hate (e.g. study biology) in order to live happily. Money is not everything, and you cannot guarantee you'll earn a lot of money even if you become a medical doctor.
If you really have the passion for mathematics, I suggest you apply at universities abroad. Apply for scholarships and fellowships and study at a place that will appreciate your passion to the field. If you really love something you'll do great at it, and I think you'll have a better chance to reach your highest potential at universities known to be strong in mathematics. Also that's where you will probably get exposed to better job opportunities.