can someone clarifiy why the more negative the electron's energy, the higher the stability? (and thus why upon ionization the electron has an energy of zero or something like that)?
Because it is lower in energy...? Lower in energy = More stable...
Think about what stability means here. It basically means how difficult it is to ionize or change states. Electrons in lower n orbitals are more stable because they are lower in energy. Think about the principle quantum number of an electron, and that E=-R/(n^2) if we treat all orbitals at some n to be roughly degenerate then the electron with the lowest energy corresponds to the the electron in the n=1 orbital. So it makes perfect sense.
Lets consider it this way... to ionize an electron in a n=10 shell is going to take photon with energy equal to E=0-(-R/100)=R/100 whereas the energy needed to ionize an electron in a n=2 shell is going to equal E=0-(-R/4)=R/4. Thus we consider the electron in the n=2 shell to be more stable. There are several ways to look at it really, but eventually it just comes down to the fact that the lower the energy=the more stable.
Would you rather be on the roof of the sears tower, or the roof of a 1 story building?
(10th orbital is sears tower and 2nd orbital is 1 story building lol)
The negative sign might confuse you but in the end, larger negative numbers are the smallest values. Therefore, they are the smallest energy values and thus the most stable.