I have been thinking about and writing about acidity for some time.
To original poster, I agree with the stronger the acid, the weaker or more stable the conjugate base (although that doesn't actually explain anything).
I have been troubled with the resonance arguments. I prefer to try to explain the effect a priori. I do not like to say, "Well, if the product of a reaction is more stable than the starting materials, then the reaction should take place." I prefer to try to explain how the properties of the starting materials enables a reaction. I think that can be done with the conjugate acids of resonance bases, but it takes more thought and explanation.
Element in same group…
That is a new one to me.
Conductive? I think this may be what I use for an inductive effect. If that is what is being referred to, then it means a through bond effect that is different from resonance. The through bond effect is how one explains the decreasing acidity of chlorobutyric acids or chlorophenols. As the chlorine is attached at a more and more remote carbon and the acidity decreases.
Re: orbital argument
I see all kinds of explanations being offered. If the acidity increases and the bond lengths decrease from C>N>O>F, does that mean the sp3 orbitals become larger? Does it also mean sp3 orbitals are smaller than sp2 orbitals and smaller than sp orbitals (again, C-H bond lengths decrease sp3>sp2>sp)? (Note, I am not accusing the poster of creating this argument, so no defense is necessary. I am merely making a comment.)
An additional comment on my comment. I think there are things that are presented in textbooks that are not as consistent as we would like. If you are a student and reading one of these textbooks, it is not unreasonable to be confused by these inconsistencies. For example, I think Pauling was philosophically inconsistent and wrong on electronegativity. He made an argument about the additivity of the energies in laying out the concept. He further said this limited the energy values. When new values that virtually disproved the concept, he changed the calculations. In doing so, he did not acknowledge that changing the calculations also changed the additivity concept (which was disproven). This results in all kinds of inconsistencies, such as trying to explain why HI should be a strong acid, or why carbon should be a better electron donor than hydrogen. Why do the textbooks always separate the carbocation stability from the electronegativity arguments? It is treated as though the electronegativity arguments don't mean anything. I much prefer a simple argument of Coulombic attraction. More protons, more attraction. Iodide is a stronger acid because it has more protons in its nucleus. Iodide is more dense, the electrons are compressed into less volume. In the alkali metals, the electrons are in the next shell and at a greater distance, weaker force, result? Cation, simple.