Understanding Analytic Signals
It's not clear what you're asking, but I think you want to know why the DFT of a signal has extra conditions for it to real. 

For the continuous case: the 2 is there because we need a function to be symmetric to have a real Fourier transform. 

In the discrete case, the DFT obey the symmtery: 

$$
X_{N-k} = X_{-k} = X_k^* 
$$
i.e. conjugate symmetry (half the values are just complex conjugates of the other half). Thus $X_0$ and $X_{N/2}$ are real numbers whilst the remainder of the DFT is specified by $N/2-1$ complex numbers (hence the 2 in the second line). 

Also, the answers to this question.

offer counterexamples to your first statement - that analytic functions have vanishing negative frequencies.