The whole thing between the flashlights...is very interesting. Here is why your notion of "seeing" velocities add up is wrong.
In our world, information seems to reach us instantly. There's no lag a car for a onto the road, and you seeing that car, which is why you don't crash into him. If you ever play video games, you know what I mean by lag...but in our world, because of how fast light travels in comparison, we see things practically in "real time." No lag.
The problem is, once you are going at very fast speeds close to light, you can't rely on this near instantaneous transmission of light/information. So even if you were going near the speed of light and flashed a light and a third observer saw, the basic reason why he won't see it going at c+your speed is because of that lag (because now it takes time for the light from him to reach us, significant amounts of time). So basically, you just can't see things, even know things, instantaneously anymore, and that creates major problems with what two people at relativistic speeds perceive.
As you can guess, time, space, and velocity are all tied into one another.
You can do the actual math calculations by doing some basic Lorentz transformations, but the intuitive reason why the work, at least to me, is because in our normal lives we assume we can see everything instantaneously. But at relativistic speeds, there is always an information lag, which screws with what we perceive to be other people's speeds, locations, and times. (location and times actually melding into spacetime but you get the picture).
Don't let the physicists get you down

as an undergrad myself, I ask a lot of "wait wtf" questions too. The only thing I'd suggest is, as the guy above said, don't make as many claims when you're actually trying to understand something because that annoys people and gets in the way of you understanding it...
once you DO understand something, (and that takes a lot and a lot of hard thought), maybe THEN you and I can make some claims =)