The capital would change places throughout the young history of the US before permanently moving to Washington D.C. This location is a sort of neutral ground between the north and south (note how it's fairly halfway between the two extremes).
Despite Columbus discovering the Americas in 1492, the Vikings were actually before him. Though I have a feeling your teacher is leaning toward Columbus considering question 4 asks about that. Also, the Native Americans were already in the Americas when both parties discovered the continents, so it really depends on how you phrase the question.
Many think that July 4th, 1776 was the date of signing, but this is likely not the case. The declaration started around this time window, but the actual signing process took place August 2, 1776.
These three ships were the ones that first arrive in the Americas in 1492. Some scholars dispute that these were the official names of the ships and they may have had other names. I have a feeling your teacher will be leaning toward the answer I mentioned above.
It probably depends on context. If you mean on American soil, then the deadliest civil war battle would be the Battle of Gettysburg (7,863 people killed). If you expand out the scope to include any American war, then the deadliest battle was The Meuse-Argonne Offensive during World War 1. About 26,277 people died during this battle. I'm defining "deadliest" in terms of the most number of people killed.
