You've been given all the exact information way back in November - Frances Jones was born 12/3/1891 and was living in Manchester in 1939.
The only anomaly is that when she was baptised it gives birthdate as 11/3.
I think you overcomplicating things by getting certificates from local register offices and getting yourself in a muddle.
You are much better off by getting your certificates from the GRO - no phone calls required, no emails. You can do everything online at:
http://www.gro.gov.uk/gro/content/certificates You can either opt to have a certificate sent to you by post or, as has been mentioned, have it sent as a PDF by email at a reduced cost of £6. The choice is yours.
You can get all the details you need for this or any other certificate on the FreeBMD website.
All you need from the index is quite simple - just enter details exactly how they are shown i.e.
Surname
Christian Name
Birth (as required right now for Frances, but another time you may want a death or marriage for someone)
Year of the event
Quarter (i.e. right now you want June quarter (Apr.-Jun.)
District of the event (in this instance Warrington)
Vol. number
Page number
Births Jun 1891
Jones
Frances
Warrington
8c
222 I've copied above the birth entry for Frances exactly how it comes up on FreeBMD - this gives you every bit of information you need to order the certificate from the GRO in just one action. No telephone calls/emails required at all - the Vol./Page numbers are for the GRO only and do not work when using local register offices. It's always easier dealing with the GRO direct online with just one simple action.
Annette