Definition of energy levels of a hydrogen atom I just want to confirm my understanding of energy levels of a hydrogen atom, since many times they introduce it without stating exactly what it is. It is given as $$E_{n} = -\bigg[\frac{m}{2 \hbar}\bigg(\frac{e^2}{4 \pi \epsilon_0}\bigg) \bigg]\frac{1}{n^2}~~~~~~\text{for }n=1,2,3...$$
Would I be right in stating that for each $n$, this is the total energy of the atom, which is basically the kinetic and potential energy of the orbiting electron? Secondly, would I be right in stating that in quantum mechanics since the idea of an electron orbiting does not really fit the idea of qm, a more accurate definition would be that this is the amount of energy you would need to remove the electron from the nucleus? Lastly, if my idea is correct that this is the total energy of the electron orbiting the nucleus then does include the rest mass energy of the nucleus and electron? 
 A: 
Would I be right in stating that for each $n$, this is the total energy of the atom, which is basically the kinetic and potential energy of the orbiting electron?

Yes and no. You should underline that the nucleus is supposed to be at rest. Then yes, $E_n$ is the total energy of the system, which corresponds to the sum of the kinetic energy of the electron and of the potential energy due to the electron/proton interaction. 

Secondly, would I be right in stating that in quantum mechanics since the idea of an electron orbiting does not really fit the idea of qm, a more accurate definition would be that this is the amount of energy you would need to remove the electron from the nucleus?

Yes. More rigously: the energy you need to take the electron to an infinitely distant point from the nucleus. 

Lastly, if my idea is correct that this is the total energy of the electron orbiting the nucleus then does include the rest mass energy of the nucleus and electron?

No, because the formula has been derived within the non-relativistic formalism, where the hamiltonian operator $H$ corresponds to:
$$
E=\frac{p^2}{2m}+V
$$
which is the classical mechanical energy.
