I don't know much about urban Africa, but in rural areas most cooking is done outside, sometimes under a roof/shade against possible rain.
Actually, there is usually a room/small hut separate from the main house, which is the kitchen
Do "jiko" and "jikoni" both mean "kitchen"? Does "jiko" also mean "stove"?
Jiko is what you use to cook. Could be cooker could be stove but jikoni is the place where cooking is done
As I understand it (although I am still just a beginner myself so don't quote me on this) the suffix -ni indicates a movement towards a place so in the context of 'The kitchen is a room' - 'Jiko ni chumba' it would be jiko while for 'I go to the kitchen' - 'Ninaenda jikoni' it would be jikoni. And yes, it does also mean stove.
No, the -ni suffix doesn't indicate movement to a place. It just indicates place. The clearest example to explain this with is nyumba, house, vs nyumbani, at the house (i.e., home). Jiko means stove. I don't agree with the course writers that this sentence 'jiko ni chumba' means 'the kitchen is a room'. If you'd want to say that, you say "jikoni ni chumba".
The contraction is wrong. Jiko is fire place, cooker or stove. Jikoni is Kitchen notice the introduction of Ni.