Say two spaceships are moving apart, both at 0.9c (relative to stationary observer) Wouldn't they observe movement faster than c? Because in realative velocities addition formula there are no "squares", therefore negative velocities do matter. So I believe the velocity of one ship relative to the other would be roughly 1.8c. (Of course I don't really believe it because nothing can travel faster than light, I would just like to know where I am wrong)

You havn't actually used the equation, have you? Put the velocities into the equation, and see what you get. It will not be >c.

No, not relative to one another, although that is what the "stationary observer" (really just a third reference frame) would see. Your error is in assuming a kind of transitive property in relative velocities. Ship A moves 0.9c relative to observer, and observer moves 0.9c relative to ship B, but you can't just add them to get ship A relative to ship B, because you would be adding measurements from two different reference frames.

You mean this equation right? (the newtonian equation, which gives 1.8c doesn't work for high speeds)

w=(u + v)/(1+ uv/c^2)

 

well set u and v both to c and see what you get. i.e. c.

Thus all objects moving at c do so in all reference frames.

 

The idea that time goes slower for objects as they approach c is what puts my mind at ease for this problem. Though I can't really explain why...