Elizabeth was born circa 1824, before civil registration so you are saying you have searched all the Plymouth parish registers, which for the Anglican churches would be
St Andrew
S Budeaux
Charles
Egg Buckland
St George East Stonehouse
Stoke Damerel Devonport
http://tinyurl.com/2ocudqThese are the churches in the outer area of Plymouth
http://tinyurl.com/2ol47hand these are the surviving non-conformist registers
http://tinyurl.com/2srntuhttp://tinyurl.com/35434oFor someone born before civil registration 1st July 1837 you would only be able to find a baptism (which may or may not give a birthdate) not a birth certificate.
If she married in the name Froud then there should be a marriage entry in the civil registration for her, but not everyone did get married and the GRO index is not a perfect index by any means.
This baptism at Greenwich would seem to indicate a marriage may not have taken place which might indicate either William or Elizabeth may not have been legally able to marry because of a prior marriage or else they simply did not choose to.
SYDNEY WILLIAM MORGAN FROUD
Christening: 27 FEB 1846 St Alphage, Greenwich, Kent
Father: WILLIAM FROUD
Mother: ELIZABETH
I think Walter's middle name was probably John.
Deaths Sep 1854
Morgan Walter John Rotherhithe 1d 827
St Mary's Rotherhithe registers are not on the IGI which is the most likely parish register to search for the baptisms of the other two known children. Those registers are held at the London Metropolitan Archives. It doesn't appear either Sydney William/William Sydney or Walter John's births were registered either as Morgan or Froud.
Regards
Valda