Tracing the slave trade through the "Dark Ages" is quite difficult, as we come up against less written sources than both the periods before and after. However, it definitely seems to have taken place. The Vikings were big slave traders. They had a habit of taking conquered people and selling them all over Europe. A prime example of this is found in Iceland - recent DNA studies of the Icelandic population have revealed they are less similar to populations in Scandinavia than people in the British Isles (particularly Ireland). Although Icelandic is a Scandinavian language, it seems Iceland must have been full of slaves taken from Britain, Ireland, and Frankia (now modern France) who adopted the language of their masters. The Vikings also took a lot of slaves from the Slavic lands - so much so that the English word "Slav" is etymologically drawn from the same root as "slave". The Vikings would also have had major contact with the Byzantine and Islamic worlds selling both furs and slaves. The high number of Islamic dirham that have been found in Northern Europe (particularly Scandinavia) point to the existence of this trade.
As for the rest of the period, slavery did continue, but with the rise of "feudalism" (I won't get into that debate here) in the 9th and 10th centuries, differentiating between a "slave" and the lowest rung peasant was very difficult, as there was not much materially different between their lives. I have heard a rough estimate that 10% of the population of England was a slave at the time of the Doomsday Book, though. In Northern Europe, the slave class seems to have integrated with the peasant class during the later Middle Ages. As most of Europe was converted to Christianity, the Church forbade taking Christians as slaves, perhaps partly because it was difficult to justify slavery and the Christian doctrine that everyone has a soul at the same time.
Slavery did continue in Southern Europe into the Renaissance, primarily due to trade between the Italian city states and the slave markets in the Aegean (controlled by the Byzantines and the Islamic world). Most of these slaves were Christians from Eastern Europe or Central Asia who had either been captured or sold into slavery by their parents.
I don't think racial prejudice had much influence on slaves and the ethnicity of slaves taken, as it was only with the boom of the Atlantic Slave Trade in the early modern period that such assumptions and ideas about race became created. As I've outlined, medieval slaves could be Irish, Anglo-Saxon, Slavic, or Greek. What does seems to have been the case, however, once Europe was Christianised, is a preference for non-Christian slaves. This ideal was not always stuck to however.
Bibliography
Jacek Gruszczynski, Marek Jankowiak, Jonathan Shepard, Viking Age Trade: Silver, Slaves and Gotland (2019)
Sally McKee, 'Domestic Slavery in Renaissance Italy', Slavery and Abolition (2008).
The second part of the question is a bit more complicated. I’ll quote a few things as explanations:
Traditional slavery had several key elements: the ownership of human beings for subsequent exploitation with the use of violence and threat, and deprivation of their liberties and freedoms. It had been a common practice since ancient Egypt and Mesopotamia.
Towards the end of the Roman Empire (Fifth and Sixth Centuries A.D.), the practices of slavery and the slave trade declined as masters/owners started emancipating their slaves. Some freed slaves for moral reasons influenced by Christianity. Others let them go as the cost of holding them was high. Some slaves were also able to buy freedom from their masters by accumulating some wealth.
After the emergence of Islam, slavery was an established institution under the Koran, and the Islamic States were among the first to acquire slaves from Africa.
The general attitude of slave traders and owners towards the slaves was not positive. The slaves were portrayed as ugly beings, infidels, or beasts and those characterisations served as a justification for the use of violence and other cruel means to maintain control over them. When slavery and the slave trade of Africans became prominent, a racial element was added to people’s perception on slavery, in that their race and skin colour were commonly identified and associated with the status of slavery. This perception of slaves was prevalent not only in Europe and the Islamic World, but also in the United States.
The United States Supreme Court made a distinction between Roman slavery and American slavery, and stated that while the former was about enslaving whites, the latter related only to black Africans. This illustrates that race was perceived as a defining element of slavery in the United States.
After the abolitionist movements, modern slavery took on different forms and characteristics: ownership and permanence were less prominent, but deprivation of life and liberty still persist to a large degree. And also the trafficked persons are subjected to labor or sex exploitation. Indentured labor became prevalent in colonized lands and much labor exploitation today even comes in the form of legitimate visa regime or labor migration regime (e.g., the overseas domestic worker visa, the kafala, the temporary migrant worker visa).
The first international legal instrument directly related to combating trafficking of modern slavery was the International Agreement for the Suppression of the White Slave Traffic 1904. Here the term “white space traffic” refers to white european women who were trafficked for prostitution. It was not only gendered (inapplicable to boys and men) but also racial.
Over the course of the past century, international law has come to recognize that explorations of labor and sex (to the degree of modern slavery) can happen to any racial group, age group, gender or sexual orientations.
Source: Obokata, T. (2006). _Trafficking of Human Beings From a Human Rights Perspective: Towards a Holistic Approach. _ The Netherlands: Brill Publishers.
My apologies if linking to a panelist's work on an off-reddit site isn't kosher for this sub, but /u/mikedash has written a piece on the medieval Crimean slave trade.