This is a very good question. For your second example, the light does actually reach B, but the paths it takes to get there are different for each frame of reference. If you are in A and B's reference frame, you could argue to be at rest and the light travels a direct path. Looking from the labs perspective however, the light moves along with the frame AB. It has to take a longer diagonal path to reach B. This means from the lab perspective time in AB appears to have slowed.
It is important to note that in special relativity everything inside your own reference frame seems normal. So it could be argued that you are always in a resting frame as long as $delta$v is zero.
So in all your examples A and B would observe a normal light beam moving between them as if they were always at rest.
Let us take a different example (from <PERSON> The elegant Universe). Imagine you had a train moving at a constant velocity with a light source exactly at its centre. 562
Now if two people stood on the ends of the train, and the light was flashed, they would both see it at the same time because the light is moving at speed c in relation to them and they are in relation to one another static. Someone on the platform that the train passes will say however that the person in the back saw the light first because they were moving towards it decreasing the length of the lights path. Who is right? Both observers are right within their frames of reference.
Speed cannot be absolute because the way we measure it, through time and distance is not absolute.
You can think about it this way: Even in normal newtonian mechanics, the velocity is relative but not because of properties of time and space but because the earth too is moving. However when you throw a ball across a field you never claim that it travels at thousands of kilometers per hour. This is because your classical newtonian frame of reference is different. If you are on something thats moving and you dont know it you might as well not be moving.
It is the equivalence between any state of uniform motion that makes it impossible for velocity to be absolute. If you can't tell whether you're moving or not, how are you supposed to tell an absolute velocity. There simply isn't a static background or frame to relate it to. 562