Essentially what you are asking about is the process of white settler migration to Africa, a process that spans literally hundreds of years and various motives, reasons, and realities. I don't usually like Wikipedia, but because of the sheer breadth of the questions you are asking and the quality of this Wikipedia page, I would really suggest having a read of the page on White Africans of European descent.

If you still have any questions that the page doesn't cover, or if you have perhaps a more specific question that you would like answering, please fire away.

Just to quickly address one aspect of your OP though - there are white populations in essentially every single African state. Indeed you would be hard pushed to find a modern African nation that doesn't have any white Africans descended from European settlers (Ethiopia possibly being an exception although, don't quote me on that). However, the reason countries like South Africa, Namibia, Zimbabwe, Tanzania, etc are perceived as having more evident white populations than others is simply that they saw larger influxes of white settlers than others. South Africa, obviously, is one of the oldest parts of Southern African to have seen white settlement, along with Luanda in Angola, and consequently the white population grew much larger and came to dominate the socio-political features of the nation more so than in more recently colonised countries, like the Congo (although there was still a large white population in the Congo Free State.)

It also depended on the European power behind the colonization, as well as the colony itself. German North-West Africa (now Ghana) had a tiny white population numbering in the hundreds, the Portuguese colonies of Mozambique and Angola similarly had relatively small white populations compared to the African population. Regional differences make it very difficult to generalise (hence my linking to that Wiki page).

It is also important to note that the location and size of white Africans today was heavily dependent upon the realities of decolonization during the second half of the twentieth century. Whether whites were persecuted by the newly independent African states (Uganda or Zimbabwe for example), or whether they were embraced or at least tolerated (Namibia or Tanzania), dictated how the white populations persisted. Zimbabwe, for example, saw its white population drop from about 450,000 in 1964 to about 120,000 in 1980 due to emigration during the War for Independence, and it continues to drop today with only a very small white population (some third or fourth generation Africans) remaining in the country.

As I say, give the Wiki page a read and feel free to ask any further questions you may have!