1) The melody from the
European Anthem
comes from the Ninth Symphony of Beethoven.
TRUE
2) The Roman Empire reached it’s largest extend in AD 116.
TRUE Hadrian came into Power in AD 117, his predecessor Trajan did not concede territories
3) Aurora, the Roman personification of the dawn, was the Roman equivalent of the Greek goddess Eos. Her sons are the Moon and the Sun.
FALSE While Aurora=Eos Eos, Selene (Moon) and Helios (sun) were siblings.
4) During World War I, over 65 million soldiers were mobilized.
TRUE I guess. I should know that as a history studend 
5) During the American Civil War, neither side used ‘colored’ troops.
FALSE What do you mean by "colored"? The Union used blue uniforms, didn't they? Does this qualify as colored? Or are you referring to African-American soldiers? There was a bataillon of them fighting for the Union too (these were not the Buffalo Soldiers that became famous later on)
6) Dutch rates of drugs use are lower than U.S rates in every category.
TRUE I guess, because it seems so unbelievable with legalized THC and all
7) The Principality of Andorra is a small nation between France and Italy.
FALSE It's in the Pyrenees between France and Spain
8) The head of the Afghan government is Hamid Karzai
TRUE He's in the papers all the time, so I guess he's the head of state for the time being
9) Armenia is an independent state. It was also the first country to formally adopt Christianity.
FALSE Armenia is an independent state of course, but the first country to formally adopt Christianity (as a state religion if that is what you mean) was the Roman Empire under the reign of Theodosius (after Konstantin who was baptized, but didn't go that far yet)
10) The ancient Egyptian god ‘Atum’ was the personification of the Spring.
FALSE God of the evening sun IIRC, I'm a bit rusty on Egypt mythology
11) During WWII, Heinrich Himmler was the leader of both the Waffen SS and the Gestapo.
TRUE [i]In the sense that you seem to mean. While he never was chief of the Waffen SS or the Gestapo directly, he was the "Reichsfuehrer SS", chief of the whole SS, which the two aforementioned were branches of.
12) Thomas Hobbes (1588-1679) was an anarchist.
FALSE "homo homini lupus" was his argument against anarchism
13) Oscar Wilde was known for his strong distaste of Americans and Gay people.
TRUE? I honestly have no idea of his private likes and dislikes. He doesn't seem like it, but again if the question is asked this way I'm going with the unbelievable