Frequency Axis of Discrete Fourier Transform (DFT) with Odd Number of Data Points
This can be answered simply by considering the definition of the $N$-point DFT:

$$X_N[n] = \sum_{k=0}^{N-1} x[k]e^{-j2\pi \frac {n}{N}k }$$

where it's easy to see that the DFT just compares your $N$-point input signal $x[k]$ to a sinusoid of frequency $\frac nN$. 

Thus, the lowest frequency is always $0$, and the resolution is always $\frac{f_\text{sample}}{N}$, no matter whether $N$ is even or odd. That also means that the lowest non-DC frequency is also $\frac{f_\text{sample}}{N}$.