1. I started as the Zulu and I couldn't build Impi... do I have to build my own embassy? What?
Yep. You now grow your civilization as you go rather than having a set one from the start. Picking Zulu only guarantees you "Native Culture (African)" which is not only a requirement for Culture (Zulu) but other cultures like Egyptian, Ethiopian, Malinese and Carthaginian.
If you have "Assimilation" setting activated then you can gain access to other cultures depending upon what cities you obtain. Such as if you took over a Japanese city then you unlock Asian civs and if you take over an Aztec city then you get access to American civs.
The full details can be found
here. Its all a mixture of what culture you start with, what terrain the city is on and what resources are nearby (sometimes even parent culture, religion, and/or civc.
In short just because you picked Zulu doesn't mean your civilization will be Zulu in culture. The world and your decisions will shape what kind of civ you will become. Note that in the future there will be many more cultures to get, even if you cannot pick their civilization to start with.
If you want to build Impi I suggest you research Warfare tech and build a city near Ivory (aka Elephants). That will guarantee you Impi at least in that city.