What’s the difference between the energy required to ionize electrons in each level and the energy that electrons occupied in each level? What’s the difference between the energy required to ionize electrons in each level and the energy that electrons occupied in each level ? To be specific, what’s the difference between the energy 1312kj/mol to ionize hydrogen’s electron and energy 13.6ev in hydrogen’s electron in the ground state ?
 A: 1313kj/mol is equal to 13.6ev(to be precise,13.598ev)
The energy electron occupied in its level is the energy required to ionize the electron.
For Instance, the hydrogen's electron in ground state has energy 13.6ev so 13.6ev or 1312kj/mol is required to ionize it and remove it. 
A: The energy required to ionize is given by that to reach bound state quantum number $n = \infty$, which is the threshold to free motion. So if the energies of the hydrogen levels are given by
$$E_n = -\frac{R_H}{n^2},\ n = 1, 2, 3, ...$$
then $E_\infty = 0$, and thus you see the energy to ionize the atom with the electron already excited to energy level with principal quantum number $n$, which is $E_\infty - E_n$, is simply the negative of the energy associated with that energy level, so for hydrogen in ground state ($n = 1$) this is of course 13.6 eV (2.18 aJ), same as the magnitude of $E_1$. The way this becomes 1312 kJ/mol is that that is the ionization for an entire mole - that is, Avogadro's number or about 6.022 x 10^23 - of atoms. Taking the 2.18 attojoules times 6.022 x 10^23 gives the energy to ionize one mole as about 1310 kJ/mol which is within rounding error (rounded to 3 sig figs) of the 1312 figure.
