Will a Nikkor 70-300mmf/4-5.6g Mount F (FX) fit and work with a Nikon D80?

Will a Nikkor 70-300mmf/4-5.6g Mount F (FX) fit and work with a Nikon D80?

Yes. It should be compatible.
If you are deciding on buying a Nikon 70-300mm lens, they make a cheap model and a more expensive good model. Don't waste your money on the cheap model. If you can't afford the expensive 70-300mm AF-S VR, the 55-200mm VR would give better value for the money than the cheap 70-300mm.

Yes. Same mount and D80 has AF motor and AE coupling for G lenses.
Will be fine.

A I have one and it's 100% compatible with my D50 & D70, as well as my semi-pro Nikons. As your D80 also has an internal autofocuing motor, you can use any Nikon AF lens with no problem.