Is a mentally ill widow of a Central govt. employee eligible for family pension?

My father died on 29th May 2010. He was a retired (March 2005) Central Govt. employee (Indian Navy). My mother is mentally ill (Paranoid Schizophrenia).

I want to know if:

1) She is eligible for the family pension?

2) Shall a bank allow us to open a pension account in her name or can it refuse to do so on the basis of her mental condition?

3) If allowed, can someone like me (42 y.o. son), be authorized to operate that account on her behalf?

Thanking you.