Who developed the concept that the total pressure of a mixture of gases is the sum of their partial pressures?.
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A chemical property of a substance is a certain characteristic that can only be observed by participating in a chemical reaction. Alternatively, a chemical property of a substance is something that can only be observed when the substance undergoes a chemical change.
I'm not sure what you're supposed to do with the first four boxes; all four are examples of chemical properties. Do you have to name the specific type of chemical property as given in the description? If so, the following would be my answers:
Flammability/Combustibility: The ability of a substance to burn.
The next two are quite strange; I'm not aware of a term that cleanly describes reactivity with water or acid. I suspect that, given the level of the material here, the general property of "reactivity" might be the answer for both the second and third descriptions
(Water-)reactivity: Some substances react when put in water.
(Acid-)reactivity: Some substances react when put in acid.
Light sensitivity: Light can interact with some things to form new substances.
As for the chart, I've filled it in as shown in the attached image. Please take care to double-check what I've written; in particular, when it comes to the property, I might have used a different term from what you were taught in class or provided in some other resource that I don't have access to. I've also color-coded qualitative/quantitative and physical/chemical for your convenience.
