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 $4a^2$) altough containing non-zero samples. For real numbers however $|a|^2 = a^2$ and the absolute value doesn't matter.

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.

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

Yes, it is because x(n) could be complex. For real numbers $|a|^2 = a^2$.

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 $4a^2$) altough containing non-zero samples. For real numbers however $|a|^2 = a^2$ and the absolute value doesn't matter.