Suppose we have the Na (Sodium) atom. It has half-filled the 3s orbital and unfilled 3p orbital. Does the empty 3p orbital have energy? also does the energy of 3p change if an electron occupy it?
Orbitals themselves are just labels for the states we can observe the electrons to be in. The electrons are what have energy, not the orbitals. So it doesn't make much sense to talk about the energy of an orbital itself. All you can talk about is the energy an electron would be observed to have it it was in a certain orbital.
Therefore, whether or not an electron is in an orbital does not change the energy associated with that orbital.
No, No, and No to your three questions.
When physicists talk about the energy of an orbital, they really mean the energy (kinetic energy plus potential energy) of an electron in that orbital. Orbitals just represent possible states for an electron. An empty orbital with no electron has no energy.
You should not think of the energy of an orbital changing when an electron occupies it, because the orbital itself is not something that can have energy.
You should think of an electron changing energy when it changes its orbital. For example, when an electron moves from 3s to 3p, it needs energy to do that, because in 3p it has more energy than it has in 3s. This extra energy has to come from somewhere, such as a photon hitting the atom.