Italy Visa Situation?

Read all about it in the website of the Italian ministry of Health below:

http://www.salute.gov.it/portale/nuovocoronavirus/dettaglioContenutiNuovoCoronavirus.jsp?lingua=english&id=5412&area=nuovoCoronavirus&menu=vuoto

USA belongs to countries in group E.

Short answer:
You can go to Italy only because of urgent reasons, work, health, or if you are a returning resident.
1. You will be able to travel to other EU countries (but not all) after you have fulfilled your 14 days of quarantine under health district surveillance.
2. Yes
3. No.
4. Yes. Unless your layover in that EU country is over 14 days. Basically if you have been in the US (Or any country in group E) less than 14 days prior to your arrival, you need to quarantine.

Also you can travel only by private transportation between the airport and your place of quarantine. In other words you cannot take trains or buses.
If you have, or have had Covid symptoms in the previous 8 days you cannot enter.

1. In theory, yes. But you need to check the local requirements as some countries recquire you to quarantine or do a test, while others do not.

And when you arrive in Italy you are to go directly to your quarantine location, not using public transportation. And your quarantine needs to be different location than with your family.

There also an app for Covid tracking called Immuni that you should download after arrival.