After reading “The Happiest Laboring Class in the World,” what are the advantages and the disadvantages that the two Virginia slaveholders give for having overseers? What are the best ways to treat slaves? What is the true nature of a slave? Lastly, why is it best to have and keep the institution of slavery? Explain the similarities and differences between the Democrats and Whigs.

These are two unrelated questions, so this response will only address the first one. The question refers to an exchange between two Virginia slaveowners in The Farmer's Register, a magazine for planters and farmers, in 1837. The magazine was an example of farming "improvement," a movement by planters to try to use better, modern methods in agriculture. But the two pieces are primarily notable as examples of the "positive good" defense of slavery that was emerging in the South as a response to the abolitionist critique that really began to gain momentum in the 1830s.
The main point of debate, as the question suggests, is about overseers. The first letter to the editor claims that overseers are not necessary for planters who provide incentives for their enslaved workers. It is full of racist assumptions about African American men and women, claiming they are naturally submissive, and as long as they are well-treated, they will not be rebellious:

His [the master's] authority should be exercised in a firm, but mild manner.I never saw any degree of courtesy shown to a negro, (that was kept under good subjection,) but was returned with usury [with interest].

The second letter claims that overseers are necessary, especially on larger plantations. He claims that overseers—as long as they are sober, honest, and held to a contract—are essential to maintaining a disciplined enslaved labor force. Still, he agrees with the other writer that enslaved people are happy ("the happiest laboring class" on earth, in fact) as long as they are well-fed and live in clean conditions. Both men assume that slaves are not fit to be free men and, therefore, that slavery is the ideal state for African American men and women.