What Does a Balance Scale Weigh? This is, I feel sure, a question I'll eventually be embarrassed about having had to ask, but:

Here is a picture of a balance scale. The black rectangle is a vacuum caused by an incredible coincidence in the random movement of air molecules.
1)  Does the balance scale tilt?
2)  If the vacuum extended all the way down to the right-hand pan, would the balance scale tilt?
3)  Is either of these questions impossible to answer unambiguously because of the non-equilibrium nature of the assumption (so that we would have to know exactly what happened to all those missing air molecules before venturing an answer)?  If so, is there some additional assumption that stands out as natural and relieves the ambiguity?
4)  Would the answers change if some force prevented air molecules from crossing the boundary of the black rectangle, so that any molecule attempting to cross that boundary and fill the vacuum is repelled outward?
 A: It doesn't tilt, at least not immediately.
The only effect of the atmosphere on the scale is buoyancy, caused by the pressure differences over its surface: if this (black rectangle) momentary heterogeneity doesn't touch the scale, then the scale won't know about it.
Until a fraction of second passes, that is. As the masses of air rush to fill the void, the wind might disturb the balance. In this sense (3) does apply, since it should influence the nature of the wind created; not to mention that if all the molecules where directed downwards, then there'd be a pressure wave hitting the plate later on.

if some force prevented air molecules from crossing the boundary of the black rectangle

That's just like having a box there, doesn't matter what's inside, there's not gonna be any difference. Though, one could argue that there is less atmosphere pushing the scale gravitationally upwards due to the empty rectangle (less mass above than otherwise).
A: The scale will tilt, if you can show there's a difference between the pressure at the bottom of the plate of the scale, and the top of the plate.  Imagining this as an ideal gas, we can think of the pressure coming from collisions of particles with the edge of the scale.  If there are fewer collisions on average on the top than on the bottom, the collisions will cease to balance, and there will be a net impulse, so the scale will tilt.  This established, it comes down to deciding if your particular scenarios will create that pressure difference.
Option 1
We have an isolated area of lower pressure that spontaneously forms.  Instantaneously, this can't move the scales - you have to consider that the information of vacuum existing has to propagate, at a finite speed. Eventually this lower pressure shall propagate out, and may temporarily cause the scales to tilt.  Whether it would or not would depend on how close the packet of vacuum is to the scales, and what the difference in pressure is.  e.g. if it was very small and far away, we can imagine by the time the pressure wave propagates, it will have a negligible effect on the scales.
Option 2
Now that the vacuum reaches the scale, we can say with certainty that the scale will tilt.  On the top side, there are no collisions with the plate.  On the bottom side, you have many collisions.  If we were doing this at atmospheric pressure, we could calculate the force due to the vacuum as
$$ F = P A,$$
where $A$ is the area of the scale where there is vacuum, and $P$ is atmospheric pressure.
Option 4
If you have a sealed box with a vacuum in it, it doesn't matter what is in that box.  Hence I don't think there will be any effect specifically to do with vacuum in this case.
I don't believe this is equivalent to attaching a helium balloon.  For one, the helium balloon is stable, unlike a small pocket of vacuum.  For two, the string that attaches the helium balloon can transmit the force of a distant difference in pressure, whereas the scale itself can only be moved by the local difference, between its top surface and bottom surface.
A: I think the situation is equivalent to creating a low pressure zone by sucking out air using a vacuum cleaner on top of the right side of the scale. Sufficiently far from the suction zone, the flow will look like that of a irrotational 3d sink flow. 
Assuming that you can measure a tilt of arbitrarily small magnitude, will the scale tilt? Yes it will, given the asymmetry in the problem statement (suction zone is not symmetrically placed w.r.t. the scale) and the fact that the flow created by the suction will definitely disturb the scale by exerting drag on it as well as a pressure difference.
So the question is to which side will the scale tilt? Since the suction zone is closer to right side of the scale the flow around the right side of the scale is more vigorous than that around the left side of the scale. Thus right side of the scale must experience a greater drag force and a consequent tilting up of the right side.
And what about pressure at the scale due to the suction zone? The radial velocity due to 3d irrotational sink flow is $V_r=m/(4\pi r^2)$, in which $m$ is the volume flow rate into the suction zone. Bernoulli equation gives $p_r=p_{atm}-0.5\rho V_r^2$. Pressure gradient at radial distance $r$ would be $dp_r/dr=+m^2\rho/(8\pi^2r^5)$. Therefore again because suction zone is placed closer to right side of the scale, right side pan experiences a larger pressure gradient that tends to push it upward.
Also above arguments imply that if the vacuum were to contained inside a rigid box then it would have no effect on the scales.
