Here is my attempt in responding to your questions.

Question # 1:
In 1860 (or any other year) BEFORE The U.S. Civil War, Were There More Free African Americans In The North Or The South?

Answer #1 - Starting with the 1830 US Federal Cenus Population Schedules up to the 1860 Census there were more free persons of color located in the slave-holding States than in the non-slaveholding States. This is my interpetation of North vs South.

In today's LunchBunch Chat Session at AfriGeneas, the discussion of the number of FPOC (Free People Of Color) in the north vs. the south was a topic of discussion.

Question # 2:
Is there any reliable data that leans towards proving that either the Southern States or the Northern States can claim to have had more free African Americans during that time?

Answer # 2- I consider the US Census as reliable in terms of who was counted as what relating to the total numbers (race/color) as reported in the above mentioned Census years to 95+ % accuracy. This is in terms of aggregate numbers and not individuals who may have been mis-classified.

Question # 3:
Should the U.S. Federal Census be the only criteria used to make this determination? If not, then how should this be determined?

Answer # 3 - Perhaps not, I'm open to reviewing other available sources to make this type of comparison. Any suggestions?

Question # 4:
Has there been any reasonable and/or reliable research to prove either/or?

Answer # 4 - For a particular year (1830) I would refer you to Carter G. Woodson's work " Free Negro Heads of Families in the United States in 1830: Together with a Brief Treatment of the Negro." There is a chart on page xx of the Introduction that lists the number of Free Negroes by State. A quick count of what I consider North vs South shows more than 200,000 Free Negroes in the South vs less than 125,000 in the North. The resonableness/reliabilty of Dr. Woodson's work is subject to the reader's opinion.

Question # 5:
Please keep in mind, that sources should be cited. Also, what reliable/reasonable criteria is being used to determine the 'race' or ethnicity of the people counted?

Answer # 5 - As a source I can refer you to the "Historical Census Browser" found @
http://fisher.lib.virginia.edu/collections/stats/histcensus/ Here you may check the Ethnicity/Race/Place of Birth for each Census year by State & County for the years in question. These numbers would have been generated using whatever criteria was used to determine Ethnicity/Race/Color by the Census Bureau for that Census year.

Question # 6:
Should only people identified (on the Federal census) as "Negro", "Black", "Colored", or "Mulatto" be considered in this study? Are the people who were charged with gathering the info on census', mostly reliable (by today's standards)?

Answer # 6 - I say yes...considering that "people of color" were probably 98% or better what we today call African-Americans. Were Census Enumerators reliable? I would say for the most part yes....I think your question refers to honesty and racial/ethnic bias and I'll leave that one alone.
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Consider too, that the records are (mostly) all we have to go by. Tell us about research that you know of, or have done.

An example of some of my research may be seen at http://familytreemaker.genealogy.com/users/t/h/o/Arthur-L-Thomas/ .... other examples may be found here on AfriGeneas within the various Forums, Databases & Mail Lists.

Thanks for the discussion and best wishes,
Art Thomas