Special power of attorney for giving flat on leave & license

My aunt, aged 82 years, owns a flat in Mumbai and proposes to give the same on Leave and License(Rent). She is old and infirm and hence wishes to grant a special power of attorney to her daughter(who also resides in Mumbai).

The scope of the power of attorney would be:

1) to negotiate and finalise leave and license agreements,
2) to appear before the sub-registrar for registration of the leave and license agreements,
3) to receive security deposit and monthly rents and deposit the same in my aunt's bank accounts,
4) to represent my aunt before the housing co-operative society and sign all relevant documents relating to the leave and license.

My query is:
a) Whether such a power of attorney must necessarily be registered, if in Mumbai?
b) What would be the stamp duty applicable, in percentage terms, if the agreement is executed in Maharashtra?
c) Is a "notarised" power of attorney valid and acceptable in a court of law?
d) What do you advise as the most appropriate course of action?

Thanks in advance for your valuable feedback and advice.

Regards/Kapil