1) During the early 1800s, many African Americans were free as a result of:
I. Manumission provided by slaveholders' wills
II. Manumission given to those who fought in the Revolution War
III. Emancipation Laws in certain states
A) I only
B) I and II
D)II and III
E) All of the above
All of these are true to some degree. Manumission was the practice of freeing a slave in your will when you died, and was a common practice by those slaveowners who had developed affections for their slaves and did not wish to see them endure hardship at the hands of another slaveowner. But due to the growing number of free blacks in southern states and the concern that created among whites afraid of uprisings, laws were passed that severely restricted the practice, so that by the early 1800s, it was more rare.
Manumission was promised for many blacks who fought in the Revolutionary War, and sometimes it was granted and sometimes not. Your question states that many African-Americans were free, but keep in mind that emancipation because of war service was also pretty rare.
The legal end of slavery in the northern states was probably responsible for the largest number of free blacks resulting from the three methods you mention, as slavery simply died out in those because the new industrial and merchant economy there didn't need them.