Can you determine the identity of an unknown substance by calculating its density and observing chemical reactions?

Yes. You can divide the mass by the volume to find its density. Density is a property that can identify a substance.

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No, you cannot! Density is not a property that can identify a substance unless you know that it is pure.

All you can do is with mass and volume is determine the density of the substance, which could be a mixture. For example, sodium has a density of 0.97 g/cc and osmium a density of 22.6 g/cc. These two metals can be combined in various proportions to give an alloy with a density with any value between the two given numbers. I am not sure how stable such an alloy might be but the point is that you could make an alloy with the same density as tin, or iron, or lead or bronze.