I think I've managed to write down the correct reaction:
$$\ce{H2O2 + KI + H2SO4 -> K2SO4 + I2 + H2O}$$
Now I need to balance this using the ion-electron method in an acidic environment.
Normally this is no problem, but I'm a bit confused on how to work with the reduction of $\ce{O}$ from $\ce{-I}$ to $\ce{-II}$ and I'm not sure how to write down the total ionic equation. I've tried the following:
$\ce{2H^{+1} + O_2^{-2} + K^{+1} + I^{-1} + 2H^{+1} + SO_4^{-2} -> 2K^{+1} +SO_4^{-2} + 2I^{} + 2H^{+1} + O^{-2}}$
But I'm not sure if that is correct, and if it is correct, I'm not sure what to do from here.
After this reaction and after diluting (with water?), I also need to know what will happen if I add a few drops of a starch-solution (I will actually have to perform this experiment so if it's merely something visible and not necessarily related to the reaction, then this part is less important.)
The final question is "what property of $\ce{H2O2}$ is demonstrated here?" and I suppose the answer to that is it's function as an oxidizer?