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Yes. No need to sum up an infinite number of zeros.

Yes, it is because x(n) could be complex. If we didn't take the absolute values of the complex numbers (Euclidean norm), a signal containing $[\dots,0,0,a+ia, a-ia,0,0,\dots]$ would have an energy of zero (instead of $4a^2$) although it contains non-zero samples. For real numbers however $|a|^2 = a^2$ and the absolute value doesn't matter.