Describe the living conditions of slaves transported by ships as a part of the transatlantic slave trade. Did slavery have a role in the growth of racism? What were the main factors in the abolition of the slave trade in the United States?

The living conditions for slaves were about as inhumane as one could imagine. Because the Africans were regarded as cargo, they were packed in the bottoms of ships as such. No considerations were made for pregnant women who gave birth on the ships, or, quite simply, for people who would need to use the bathroom. As a result, for weeks, human beings were forced to lie in their own blood, feces, urine, and vomit, as some of those transported became ill due to illness or from being overwhelmed by the smells.
Slaves were packed very tightly into the bottoms of ships. The goal of the traders was to fit as many bodies in as possible. Mere inches of space separated one captured individual from another. More space was allowed only in instances in which a slave committed suicide by jumping off of a ship, or when those who had become too ill to be sold were forced overboard.
Every few days, slaves would be brought out onto the deck of the ship. Here, they would get exposure to sunlight and were allowed to breathe fresh air. Traders would get buckets of freshwater and throw the water onto the slaves. This was a feeble effort at maintaining hygiene. They were allowed small amounts of food (e.g., manioc, fish) and water to drink.
Slavery certainly had a role in the development of racism. Arguably, if Europeans had simply admitted that they captured Africans out of economic necessity (attempts to enslave Native Americans had failed over the long-term, and white indentured servitude was deemed less economically viable), perhaps some future troubles could have been avoided. It was the need to justify the act of enslavement which caused the racial tensions and hatred that remain prevalent today.
Racism had developed as a pseudo-science in the eighteenth century. Those who studied anthropology and biology began measuring skulls to determine differences between groups of people. It was assumed that the skulls of those of African descent showed evidence of poor mental development. With this, many whites came to believe that blacks deserved enslavement because they were deemed mentally inferior to whites.
Of course, not every white person believed this. There were some who believed that slavery was morally wrong and inhumane. A few even went as far to try to have it abolished, which was the purpose of the abolitionist movement.
It would be incorrect to think that the movement was popular. Though slavery did not exist in the North after the early nineteenth century (New Jersey was the last to abolish it in 1804), Northerners were not exactly more enlightened in their views on race. The popularity of minstrel shows in Northern cities in the 1830s and 1840s is proof of that. 
It would also be incorrect to think that everyone who detested slavery viewed blacks as equals. This was also true of some abolitionists. One of the causes of the rift between Frederick Douglass and William Lloyd Garrison was Garrison's stubborn need to use Douglass as a symbol of his cause instead of viewing Douglass as a peer in the movement.
The slave trade was abolished in the United States in 1807. Great Britain followed suit, abolishing its trade a year later. Other Western nations would continue to perpetuate the trade, including Spain. 
The assumption among some members of Congress was that the abolition of the trade would lead to the eventual discontinuation of slavery in the South. This proved to be untrue. Slavery would not end in the United States until President Lincoln delivered the Emancipation Proclamation in 1863. Until then, to whet its appetite for more slaves, traders and planters forced the breeding of slaves, often raping black women themselves to force pregnancy. Also, free blacks from the North were sometimes kidnapped and brought to the South to be sold.