Regarding #1, the oscillator strength is defined for an optical transition between two particular electronic states, see
https://en.wikipedia.org/wiki/Oscillator_strength. The standard ATK output for the Optical Spectrum is the susceptibilty and dielectric tensor, given by the Kubo-Greenwood formula, see Notes in the reference manual
http://docs.quantumwise.com/manuals/Types/OpticalSpectrum/OpticalSpectrum.html?highlight=optical%20spectrum#NL.Analysis.OpticalSpectrum.OpticalSpectrum. The oscillator strength between state n and m is essentially given by the dipole matrix elements (pi_nm) in the Kubo-Greenwood formula.
Regarding #2, I would say it usually works other way. One first defines the transition of interest, i.e., state n and m, and then calculate the corresponding oscillator strength for that transition between these states. If the oscillator strength is zero, the optical transition is forbidden. If you have a full dipole matrix, you may then identify those transitions (states) that are optically active, i.e., have non-zero oscillator strength.
Regarding #3, HOMO and LUMO are just two states, and one may calculate the oscillator strength between HOMO and LUMO states, i.e., n=LUMO and m=HOMO.
The dipole matrix elements (oscillator strength) are not a part of basic output for Optical Spectrum analysis.
