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".
My understanding is that the -ni is similar to a positional preposition. Nyumba is house, nyumbani is 'to the house' 'in the house' 'into the house' etc. Same with jiko. Jiko means stove or kitchen, so jikoni is 'in the kitchen' 'to the kitchen' 'on the stove' etc. And I'd like to add to the consensus that jiko can definitely be a room, as the course indicates.