Yes, that is perfectly fine. (in c++ at least)
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The value of the variable in the base period forms the basis of comparison of the variable in other periods.
The best known CPI is the Consumer Price Index and that cannot be negative.
If, by CPI, you mean the consumer price index, the answer is not unless people are paid to take things away from shops!
No. This would imply that the speed of light in that medium was greater than the speed of light in a vacuum, which is physically impossible according to the theory of relativity. The relative index of refraction can be negative... that is, the speed in the medium may be faster than the speed in the surrounding environment... but the absolute IR cannot be negative.
the index of a cube root is 3.