Sampling of a band-limited analog signal: DFT and aliasing
The provided answers are correct. Appending zeros is not upsampling and therefore the sampling rate is still $R_\mathrm{s}=100\, \text{Samples/s}$. Accordingly, the frequency spacing after taking the N-DFT is $f_\mathrm{d}=(R_\mathrm{s}/N)=0.25\, \text{Hz}$.

Upsampling can be achieved by inserting $N_\mathrm{U}$ zeros after every sample followd by lowpass filtering.