We study the ground state of $N\gg 1$ noninteracting fermions in a two-dimensional harmonic trap rotating at angular frequency $\mathrm{\Omega }>0$. The support of the density of the Fermi gas is a disk of radius $R_e$. We calculate the variance of the number of fermions, ${\mathcal{N}}_R$, inside a disk of radius $R$ centered at the origin for $R$ in the bulk of the Fermi gas. We find rich and interesting behaviors in two different scaling regimes, (i) $\mathrm{\Omega }/\omega <1$ and (ii) $1-\mathrm{\Omega }/\omega =O(1/N)$, where $\omega$ is the angular frequency of the oscillator. In the first regime we find that $\mathrm{Var}{\mathcal{N}}_R\simeq (AlnN+B)\sqrt{N}$ and we calculate $A$ and $B$ as functions of $R/R_e$, $\mathrm{\Omega }$, and $\omega$. We also predict the higher cumulants of ${\mathcal{N}}_R$ and the bipartite entanglement entropy of the disk with the rest of the system. In the second regime, the mean fermion density exhibits a staircase form, with discrete plateaus corresponding to filling $k$ successive Landau levels, as found in previous studies. Here, we show that $\mathrm{Var}{\mathcal{N}}_R$ is a discontinuous piecewise linear function of $\sim (R/R_e)\sqrt{N}$ within each plateau, with coefficients that we calculate exactly, and with steps whose precise shape we obtain for any $k$. We argue that a similar piecewise linear behavior extends to all the cumulants of ${\mathcal{N}}_R$ and to the entanglement entropy. We show that these results match smoothly at large $k$ with the above results for $\mathrm{\Omega }/\omega =O\left(1\right)$. These findings are nicely confirmed by numerical simulations. Finally, we uncover a universal behavior of $\mathrm{Var}{\mathcal{N}}_R$ near the fermionic edge. We extend our results to a three-dimensional geometry, where an additional confining potential is applied in the $z$ direction.