It was hard for me to understand this arbitrary rule of things becoming less ordered over time. Was this just a fundamental natural law?
The answer is no. Entropy is a logical consequence of probability and time.
Why do things become more chaotic over time? Because chaotic configurations have a higher probability of occurring.
There are far more disordered configurations of things then there are ordered, this is why things become more disorder with time. Time changes the configuration. And by probability a high probability configuration is more likely to occur then a low probability configuration. So the axiom of nature here is not entropy, it's probability. Entropy is just a consequence of probability.
There are systems where ordered configurations are more numerous then disordered configuration and in those systems things become more ordered with time. In these cases entropy is STILL defined to be increasing as things get more ordered. Thus entropy is not describing disorder, or is it?
The thing I don't fully understand yet is heat entropy. Apparently when you take heat into account for everything, the disordered intuition suddenly becomes applicable. So if you have a system becoming more ordered with time, heat must be increasing somewhere to offset this increase in order. Maybe someone can explain this part to me?