E isomers are more stable than Z isomers due to steric reasons
This is not always (but usually) the case and it's not
just an issue of sterics, to my knowledge. One isomer is favored over another because of an increased net-dipole moment that arises from the arrangement of the molecule. E isomers usually have some kind of hydrogen IMF which makes them more favorable. But you're right, steric hindrance is one reason E is favored.
HOMO/LUMO helps to explain the shape/hybridization of the electron orbital cloud and the reactivity of the orbitals.
HOMO/LUMO help explain why conjugated alkenes are so stable. Actually, it's for the exact same reason you mentioned for the stability of aromatic rings - the overlapping network (adjacent) pi bonds. The adjacent pi bonds contribute to an overall lower energy which increases the stability of the molecule.