Ciao Corinne,

in Italian, just like in Dutch, there’s no difference between “among” and “between”. We use the same word “fra” (or “tra”), which can either be used as “among” (for example: una casa tra gli alberi, a house among the trees) or as “between” (for example: un bambino tra sua mamma e papà, a child between his mom and dad).
“In mezzo a” can mean “among” (una casa in mezzo agli alberi, a house among the trees) or “in the middle of” (un gatto in mezzo alla strada, a cat in the middle of the road) and in this last case it has the same meaning as “al centro di” (un gatto al centro della strada, a cat in the middle of the road).
You’ll get used to all these different uses with practice, don’t worry.

As for the sign you saw, it was for sure “Divieto di caccia” (divietato doesn’t exist). Divieto is a noun, not an adjective. It means prohibition, not prohibited, and it’s kind of formal. It’s used mostly on signs, legal documents, etc. So for example, on a sign you’ll find “Divieto di caccia” which means “In questa zona c’è il divieto di caccia” (Literally: In this area there’s the prohibition of hunting). Or you can find “Divieto di balneazione in questo lago” (You can’t swim in this lake), and so on.
In everyday Italian, we don’t use “divieto di”, but we say “è vietato” or “è proibito”. So: è vietato cacciare; è vietato nuotare; è proibito fumare… and so on.

I hope I helped you with your doubts. If you have any more questions, I’ll be happy to answer 🙂

Carmine 🙂