There are still lots of Indians in Tanzania and Kenya, they never fully left and either mixed with the locals or formed their own communities. I was in Africa earlier this year and a lot of the Indian culture is still there. Similarly, Durban and many of the other large cities in South Africa still have sizeable Indian populations. In Zanzibar, they have their own architecture like the Zanzibar door, where door decorations reveal the ethnicity and sometimes the social status of the owner. Square doors represent Arab or African ethnicities, as the Arabs brought them over and the Africans later copied them. The arched doors are owned (or were at one point built) by Indians, and are often studded with metal spikes in the Indian tradition to prevent Elephants from leaning against or hitting them. Zanzibar elephants have disappeared since the early visits of Marco Polo, but the spikes and many of the carving patterns were kept for the sake of tradition.

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From what the locals told me, the small businesses are mostly owned by local Indian families, as the Zanzibar Indian culture is more commerce-oriented than the Swahili African one. I'm sure Indians did all of the above that you mentioned, but from what I have seen, they are still a distinct and fairly significantly-sized portion of the former colonies.