Let me take your easier question first. We cannot and do not pretend to "judge speed on a universal scale". The basic assumption of Special Relativity is that you can describe things from the point of view of any inertial (non-accelerating) observer using exactly the same laws of physics. That means that any one of those observers could say with equal justification that he was at rest.
Now what happens to stuff that is traveling quickly, according to us? As you surmised, all processes on that traveler happen slow, according to our assignments of times to the events on the traveler. But wait- from their point of view, it's us
who are traveling. Does that mean that from their point of view, it's our events (watches, heartbeats...) that are running slow? Yes, exactly. From your own point of view, it's them
who is traveling fast, and that doesn't affect your clocks.
How can that be consistent? If the observers have fixed velocity with respect to each other, the distance between them keeps changing. The lengths of time it takes to observe events on the other keeps changing. Each observer must allow for that length of time in calculating when things he sees happened at the other one. However, because each observer treats the signal as traveling at the speed of light with respect to himself
, not the other observer, they disagree on those observation-lag corrections. The sum of that disagreement and the disagreement about how long the events are taking just cancels out. So it's all self-consistent.
Now you might wonder about observers circling each other at fixed distance, where the signal time doesn't keep changing. Something else must be going on. Yes- that's the path to General Relativity, also self-consistent but even stranger.
Finally, what about your philosophical question on the meaning of time? It sounds like you and your wife came to a nice working definition.
(published on 04/15/2011)