special relativity - Clock in a sealed box at half the speed of light. How would it know it is moving?

Consider a clock enclosed in a sealed box here on earth syncronized with my wrist watch. I send the boxed clock around the galaxy a couple of times at half the speed of light (or the full speed of light..). I hear that the clocks will be out of sync when the boxed clock comes back on earth.

Is that true?
How would the boxed clock know it was moving when it was actually stationary in reference to the box?
I hear explanations about how when traveling from point A to point B, time and space became one. I do not understand that, but that's besides the point. In this question point A is same as point B. So the clock has come back to where it started. Does the time for the moving clock somehow come back to be in sync with the wrist watch ?
Would the effects of departing the earth at c cancel out because of the effects of approaching when the jurney is over?