Is it possible to slow down the speed of light in a vaccum?
The answer depends on what you mean by "vacuum", and then it also depends on what speed you have in mind.
If by "vacuum" you mean "far away from any matter" then the answer is no: it's not possible to slow down the speed of light.
If, on the other hand, by "vacuum" you mean "there's nothing there except electromagnetic radiation, but it could be quite close to other stuff such as a nearby piece of glass or some conducting surface" then the answer depends on what you mean by "the speed of light". If you mean "the speed at which electromagnetic energy and momentum is moving along" then it can easily be slow. But if you mean "the speed limit implied by the intrinsic geometry of spacetime" then no, that doesn't change.
No, because the speed of light in a vacuum is defined as 299,792,458 meters per second.
This means that the sort of things one might think about to change the speed - say general relativistic warping of space and time - are given a "back seat" to the speed itself. So, some sort of exotic warping would change how long we thought a second was in that piece of space-time, or how long we think a meter is. We prefer this because the speed of light appears at at very fundamental level in key physical equations - like, for example, Maxwell's equations.
It is quite a vague question. First, far from a compact source, the emitted light propagates away with $c$, but close to a source (which is a set of charges) the resulting wave may have a complicated structure due to closeness to a distributed in space source. For (an extreme) example, the wave in a wave guide (i.e., next to the conducting walls) a wave propagates differently than in a "vacuum" just because it is a result of emitted wvas from differently spaced sources.