Hi
This is a tricky question so don't worry if you are struggling with it at the moment. In an actual exam, I suspect the wording would be a bit more straightforward.
Im not sure your plan is the right way of going about answering the question at the moment. As a starting point for thinking about positivism, you should write about Auguste Comte. He was the (sort of) first person to say that the social sciences should try and study things in the same way that the natural sciences did. (Natural sciences being chemistry, biology and physics etc.) Durkheim carried on this and suggested that there was a real-world that could be studied. So if we take science to be a way of studying the world through the gaining of empirical facts, then yes Sociology is a science as this is what positivists are trying to achieve. Positivists are trying to gain empirical information about the world. If you want to use Durkheim's study of suicide at this point go ahead but it isn't necessary (in my opinion) for this question.
Then refer to what Kuhn says about paradigms, this is a nice segway into interpretivism. Sociology does not have one central paradigm, so if we take Kuhn's view of what science is then Sociology cannot be a science. Interpretivist rejects the idea that the social world can be studied in the same way that the natural world can be studied. This is for lots of different reasons
1. The researcher cannot separate themselves from the social world, this is because they are a product of the social world.
as a way of explaining this, a chemist has no preconceptions or biases toward Metal, because metal exists in the natural world rather than the social world. Interpretivism rejects the idea that you can be truly objective in your study of the human world.
2. The scientific method is not suited to studying the social world.
I would frame this point as being simply that interpretivists do not care if Sociology is a science, as the scientific method is not suited to studying society anyway. They take the view that the world is something that is constructed socially, in the minds and interactions of the individual. Meaning it does not objectively exist as the natural world does. So trying to apply the scientific method to something that does not objectively exist is not appropriate.
Popper and falsifiability does not neatly fit into what I have just said, so I'm not sure how it fits into the structure.
I hope this helps a little, any other questions then let me know.