"Molina" is a very common toponym.
My guess is that it was initially used to mean a place with a mill, and was then extended to a whole village.
Mulino=Mill, hence the surname Molinaro=Miller.
I want to add that, in this case, the correct reading is "Casalis Molinae", with the final diphthong ...

Giovanni Ciro Gaetano, son of Leoluca and Francesca Finocchio.
Next time, please tell us what record you are referring to!

Mary,
this baptism is for Paolo Serafino Giovanni, son of Antonino and Giuseppa
the marriage record was for Antonino, son of Gaspare and Vincenza
So, there seem to be no contact between the two, except the surname

Date of baptism "under condition": Oct 14, 1731
Paolo Serafino Giovanni, son of Antonino, and Giuseppa Cella (?), born on day 12, and already baptized by the midwife.
Godparents were Giacomo Di Puma, and Anna Maria, Giovanni Murdello(?)'s wife

Hi Mary,
marriage date is Sep 29, 1726 ("29 eiusdem" = "of the same")
Groom: Antonino Briganti, son of "master" Gaspare, and of Vincenza Briganti (but this could be her married name)
Bride: daughter of Giuseppe, and Filippa Papania (also, this must be her married name)

In my opinion, they are not, as they are minor children of an Italian citizen.

Jun 10, 1728
Filippo Messina, born in Militello, living in this town (Mineo), and Anna Capra, never married, daughter of deceased Florestano Capra, and living Giuseppa Vinciguerra.
Filippo's parents are not mentioned

If you and your daughter achieved your citizenship, you won't be deprived of it. It is what in Italy is called a "diritto acquisito".

What's you GGF's name?
It might help to identify the area

Francesco Siconolfi, 61 years old, son of deceased Nicola, and Antonia D'Ambrosio, died on Jul 28, 1872, in jail in Genova.
The Director of the prison sent a note about the fact to the Comune of Genova, and the Comune of Genova to the Comune of Guardia Lombardi. It doesn't say where Francesco was ...

“"Industriante" is a word that takes on different meanings according to geographical area. In the south, it was also were people who rent large plots of land from richer owners, and the had peasants work for them.
In the north, it was more used to mean a laborer, or a person who did not have a ...

What part, exactly?

I think it's accurate enough for someone who is related to reply.
You only should translate it to Italian before posting.

No, in Italy you can't get BMD records before 70 or 100 years, depending on the cases, for privacy reasons.
If you know where he was from, you contact some local group on social networks to ask if someone knows him or his descendants.
For instance, on FB such groups are often named "Sei di <town ...