Obs: since you deleted your picture, I'll add this structural diagram to help point out to which nitrogen atoms I am referring to.
The correct answer to this question is more direct, and not listed in your items. The non-bonding electron pair in nitrogen $3$ is in an orbital perpendicular to the $\pi$-bonding $p$ orbitals of all other atoms in the imidazole ring. Thus, it does not have the appropriate geometry to overlap with other orbitals forming $\pi$-bonds, and does not participate in any resonance effects.
This effect of orbital geometry is often invoked to explain the difference in basicity between pyridine and pyrrole. In the former, the nitrogen lone pair is of type $3$ and does not participate in resonance, and so it has a basicity comparable to regular amines and imines. However, in the latter, the lone pair is of type $1$ and does participate in the aromaticity of the ring. Protonation of the nitrogen atom would require localization of the electron pair on the nitrogen, breaking most of the resonance effect. This is energetically unfavourable, so pyrrole displays a much lower basicity than expected for amines or imines.
This section on pyridine has a little more information on why the type A lone pair does not delocalize, including a helpful picture. Notice that the lone pair is in an $sp^2$ orbital parallel to the plane of the ring, while the $\pi$-bonded system is perpendicular.
Edit: In response to the comments, I can make the following observations on your conjectures:
1) I don't think this applies, actually. The fact that orbital overlap is disallowed in the first place precludes the possibility of even thinking what would happen to the geometry of the molecule if the electron pair in nitrogen $3$ formed a $\pi$-bond; it just doesn't.
However, if the molecule had a boron atom instead of carbon in position $2$ (with an empty $sp^2$ orbital pointing in the same direction as the full $sp^2$ orbital in nitrogen $3$), then I'm not sure what would happen. A more simple example of this type of structure would be 1,2-azaborine (of which only the 1,2-dihydro derivative seems to have been isolated as of yet).
I could imagine canonical structures in which the electron pair on nitrogen links with the boron atom, forming an additional bond (analogous to benzyne, which is isoelectronic with 1,2-azaborine). However, to form an extra N-B $\pi$-bond, then either the bond will be a $\pi\ (sp^2-sp^2)$ bond (which is unusual as far as I know), or both the nitrogen and boron atoms would have to partially rehybridize into a mix of $sp^2$ and $sp$ configurations to allow a $\pi\ (p-p)$ bond, which would likely imply an increase in bond angle and a huge increase in ring strain. Neither option seems particularly good, so I suspect such canonical structures would contribute little to the actual bonding picture in the boron-substituted ring.
2) The nature of the nitrogen atom which participates in resonance is actually something between $sp^2$ and $sp^3$. The concept of hybridization isn't very adept at explaining resonance naturally.
I'm also not happy with how much my arguments rely on hybridization, but I don't know other effective means to explain what's going on.