I was thinking if I built a device with 7 clocks, synchronized to each other, one in the middle, one up, down, left, right, behind and in front of me, say 1 meter away, and I fired a laser from the middle and split it into six pieces would the light always arrive at all six "corners" at the same time?

If we accelerated (say to the right) up to half the speed of light and fired the laser again, wouldn't the laser have to travel farther to reach the right sensor (as it's moving at half the speed of light) and travel less distance (as it is approaching the light at half the speed of light)? So the time the light arrives at the right sensor should be greater than the time it takes to arrive at the left sensor.

I'm assuming you will tell me that this is not true, the light will still arrive at all the sensors at the same time. Why would this be true?

Isn't the whole apparatus moving at half the speed of light in one direction? Why would that make no difference? In that case, why couldn't I just accelerate to half the speed of light again, to the right? (Then I will be going at the speed of light - half the speed of light, twice, but in each instance I was considered to be standing still.)