When I was at Milan University 40 years ago the more attractive students were still "bambine" (no PC in those days!).
In general a "bambino/a" was an infant or little child and became a "ragazzo/a" about the time of leaving primary school. "Fanciulla" I only ever saw in literary texts and we generally translated it as "damsel". I am uncertain why D/L keeps wanting "baby" for "bambino/a" as these were always described as "neonato/a".
Please bear in mind that these comments refer to Milanese usage from 40 years ago and may have changed since then or be different elsewhere in Italy!