[llardicus]

Based off the bonder order of 1, F2 has a single bond, and its HOMO is pi*. I get how to fill in the MO diagram, but I do not see how it is supposed to tell me that its bond is created by the 2P orbital through sigma bonding. What am I missing here?

[Enthalpy]

Atoms have several 2p orbitals. Do you already have a clear understanding of that? Only two (2) electrons per orbital.

As for deeper orbitals, they do interact as atoms get closer to an other, but
- Smaller orbitals, here 1s, interact little because they are too faint at one atomic radius
- More refined : the interaction takes place and creates molecular orbitals, but one has an energy smaller than the atomic one, the other a bigger energy, and the change is nearly as big, so this cancels out. As the atomic orbitals were full and so are the molecular ones, the interaction is a null operation, so it's not counted as a bond.

Then you could consider the shapes of the orbitals and how well they fit an oriented bond.