Your error is in the idea that because you are still and can see someone moving, everything that they see is slower. That's not quite the case. Weirdly, the light will move away from the two of you at ...

Weird thing about light; it doesn't really follow Newtonian mechanics. So we can fire something in a specific position to where we will be such as some planes being able to shoot themselves down. ...

Short answer: It depends... Long answer: ...on what you're measuring. Take your example about the earth moving and the sun moving through the moving galaxy. We can take our frame of reference to be, ...