Finally, a question I can answer! I’m going to answer the second part of this question first, because it’s what I’ve done the most research on.

When Columbus first visited the shores of what came to be called the New World, the residents of the region had already domesticated and cultivated the chile (in a prime example of the European tendency to relate New World imports to foods they were already familiar with, Columbus and his fellow explorers ended up naming the chile after an unrelated but also spicy plant from the Caucasus, black pepper, thus giving chiles the misnomer “peppers” that they still carry today). Evidence of chile cultivation in Central and South America dates back to 5200 BCE, placing chiles among the oldest cultivated crops of the Americas. I mention this early cultivation in order to drive home the fact that there were dozens, if not hundreds, of varieties of chile that were actively being grown by Native Americans in the 15th century. Similar to the continent of Africa, the continents of North and South America extend vertically more than horizontally, and encompass multiple latitudes and growing regions, including equatorial. Due to the widespread and long-standing cultivation of chiles across these multiple growing zones, there was basically guaranteed to be a chile varietal that could grow anywhere in Africa. While Africa is a huge continent that contains many different regions and biomes, so, too, is America, and America was already full of chiles -- they made the crossing easily.

The introduction of chiles to Africa rests mostly on the shoulders of Portuguese spice traders, who had existing trade routes for Far-East and Indian spices. Because of, well, the existence of the continent of Africa, these Portuguese trade routes basically just hopped around the eastern, southern, and western coastlines of Africa until they could get to India, playing connect-the-dots with a number of major African port cities. Once Portugal gained access to New World crops in the late 1490s, they disseminated them along these existing trade routes with “almost unbelievable rapidity.” We’re looking at under a decade from “discovery” ^((scare quotes because the native Americans obviously already knew about chiles)) to basically the entire perimeter of Africa having chiles. And chiles, unlike a lot of other spices, are very, very easy to grow to maturity from a single seed. In contrast, black peppercorns are the dried immature seeds of the piper nigra plant, and cannot be sprouted or grown. Many other spices take years to achieve maturity enough to harvest; ginger, for example, takes 2-3 years to grow a crop from a single rhizome, and Sichuan peppercorns fruit on a similar timescale. Chiles take mere months. The speedy growing timeline and the rapid dissemination of seeds, as well as the chile’s many varieties, create a perfect storm of qualities for sudden spread across the African continent (and Indian and Asian, but that’s unrelated to OP’s question).

I can speak less to the impact chiles had on African cultures and customs. In general, chiles were easily adopted by the multicultural cuisines of these port cities, who were already used to trading in spicy and pungent elements such as black pepper, Sichuan peppercorns, and ginger. The accessibility of the chile, once introduced, allowed poorer people to finally use these spicy elements that were previously the provenance of the elites, which contributed to the spread of chiles outside these wealthy port cities. Aside from food, there is some evidence that chiles (often called capsicums in this context) were used in dyeing fabric in African textile traditions.

In short, the adoption of chiles was so widespread across Africa because chiles were biologically suited to be grown in multiple regions of Africa, because they were easy to propagate, and because they were introduced quickly via Portuguese trade routes to basically all the major port cities of Africa at once. The integration of chiles probably had a small but exciting effect on existing African cultures, given that they were introduced first to cities used to integrating foreign foods and customs. That said, if anyone else can speak further to the cultural context of African port cities circa 1500 CE, please do!