Anything that is not restricted by the TSA to be shipped with you.
No.
It is safe. Hundred of US citizen travel daily to Serbia.
The right to travel with a US passport is one benefit of being a citizen of the US. US citizens need a passport to travel to other countries.
May be Afghanistan is the only friend country for USA, in which US citizens need Visa to travel.
no
Passports are not required for travel inside the US. Anyway, non-citizens, legal or not, are not eligible for US passports.
Only in the US and it's territories.
All countries in Europe
Yes
Indeed.
This will depend on where you want to travel. If only within US then you need a valid ID, if international travel you need you passport, visa and other requirements like immunization and such.
No, US citizens do not need a visa to travel to Romania. I myself have been there three times. Romania is a part of NATO. Any country that is a part of NATO US citizens do not need visas to enter. US Citizens need a visa if they wont to travel to Russia. I was in Frankfurt and some American didn't have a visa for Russia. The Airlines flew him to Russia but when he landed the government put him on the first flight to Frankfurt and deported him.