British Passport renewal PIO query

[query101]

I have recently applied for renewal of my British Passport
in Bangalore India.I have my PIO.I reside in India.

Can I leave India with my updated Passport,
residential permit and PIO (both PIO and RP
have my old Passport number) and off-course
the old passport ?

When I receive my
Passport- (on an Indian residential address.), how do
I update my PIO ? how long will this process take ?
Is it better to get my PIO updated in UK ?