How can there be electrons in the Fermi level?
From Wikipedia:


  The Fermi-Dirac distribution \$F(\epsilon)\$  gives the probability that (at thermodynamic equilibrium) an electron will occupy a state having energy ϵ.


That is, the Fermi-Dirac distribution doesn't give the probability of the existence of an electron at a certain energy. Rather, if there is a state at that energy, it gives the probability of the state being occupied.

So if there are no states, there won't be any electrons regardless of the Fermi level.