1. Adopted girl >from Florence

I am wondering if anyone would know how I could find out
anything more about the chances of a Jewish baby girl >from
Florence being adopted in Manchester in that period.

Do you mean Florence (firenze) in Italy?
If yes, there was an Hospital or nursery called
"Istituto degl'Innocenti" who was in charge of the care
of abandoned babies and to give them in adoption.

The archive is very rich of registers and documents:
http://www.istitutodeglinnocenti.it/?q=content/archivio-storico
In same cases researchers have connected their family to the
mother who abandoned their babies, after hundred years.
But the Italian adoption is probably not the origin of the
Jewish blood of your g-grandmother because the Jewish
communities were very careful not to lose their babies.
An illegitimate Jewish baby would have kept in the Jewish
community and the mother would have helped not to abandon it.
I often found in Tuscany records of birth of Jewish babies
with "Father unknown". They simply lived with the mother.
On the Jews in Firenze please see my:
http://www.italian-family-history.com/jewish/Firenze.html

2. NUNES CARVALHO family
Dear Keith and Nancy Atkinson

We are now documented back to Abraham NUNES CARVALHO
born Portugal abt 1650 who married Sarah about 1680 and
had Isaac in 1681 in Oporto, Portugal.

Which is the source of this information?
The family was active in Livorno. Isaque Nunes Carvalho
is listed in a census of the 18th century.
Livorno town had very strict links with Amsterdam.

Nardo Bonomi (Braverman)
Greve in Chianti - Firenze - Italy
Researching on:
BRAVERMAN >from Podolya
GROBMAN Ukraine
LUFT and GRUNBLATT Kolomya
OCCHIPINTI anywhere