This is kind of a huge question. I can at least give a basic explanation connecting them.

At the time of the arrival of Columbus, the Antilles were largely populated by people of Arawak descent. Arawak speaking peoples had traveled from the Amazon to Northern South America (modern Colombia and Venezuela) and from there to the Antilles. Not getting into the issue of how best to name the peoples who lived in the Antilles (Taino, Caribs, etc.) since that's a huge debate in and of itself (see Corinne Hoffman & William Keegan: The Caribbean Before Columbus).

The Caribbean was populated by indigenous peoples from multiple regions thousands of years ago, with the Taino peoples arriving around 500 CE or so and the Caribs of the Lesser Antilles more recently than that. They appear to have traded with each other and with both civilizations along the coast of Northern South America and Meso America. It also appears that some regions, such as Western Cuba (the Guanahatabey people), were originally with Florida and may have traded with that peninsula. There were also economic specialization, such as the harvesting and trade of special colored shells from the Turks and Caicos islands to the North of Cuba and to the East of Southern Florida.

Much of the nuance and connections of this world was lost during the conquest, especially given that they were peoples who had yet to discover writing. A fair amount of what we know about the peoples who faced the full brunt of early colonization (such as the Taino of the Greater Antilles) is through European chroniclers (such as Bartolomé de las Casas). This skews our understanding, since we must depend on information being mediated by outsiders who often do not fully understand local languages or customs. Other sources, like Columbus' diaries, also have issues such as him writing about the peoples he met based on the assumption that he was Asia.

I can't speak as much for the Lesser Antilles, but in the Greater Antilles, indigenous foods have survived into contemporary times. Cubans still eat Taino casabe bread (yucca bread), for example.

The major relationship between indigenous peoples and people of African descent was that the scarcity of indigenous labor, or the propensity of indigenous peoples to successfully flee into the jungle or forest, led to colonizers seeking African labor. At first they made attempts to simply kidnap indigenous peoples from elsewhere in the Caribbean. Yucatec indians were kidnapped from Yucatan in the 16th century and brought to Havana to work, for example. But these raids were costly and required a great deal of manpower. Instead, it was simply to trade with African polities along Western Africa.

As John Thornton pointed out in Africa and Africans in the Making of the Atlantic World, 1400-1800, the Portuguese were unsuccessful in raiding the African coast during this early period. They kept being killed when they tried to go inland, so instead they traded for slaves captured in war.

Africans came to the Americas to replace the indigenous peoples as the subjugated workforce of the region. The colonizers who arrived in the Caribbean weren't coming as settler-colonists, setting up individual farms, but instead were trying to reproduce something similar to the lord-serf relationship existent in Europe; a dependent laborer population.

I'm aware that Africans and indigenous peoples mingled at various points during the colonial era. I've also seen mentions of this happening more frequently in the Lesser Antilles, where resistance to colonial control lasted longer because the smaller islands in the South-East were only colonized much later. But that's all outside of my wheel-house.

I know this doesn't fully answer your question, but I hope it at least gives you some basic info.