Originally Posted by GM4Him
So, even computers obey laws. Laws dictate what the computer can do and how it behaves. No video games would even exist without said laws. Likewise, our universe is similar. It would not even exist as we know it without laws to govern it.
Dude. There's a big difference between physical laws like gravity, and man-made socially constructed laws that govern societies. It is the latter that is relevant for D&D alignments.

Originally Posted by GM4Him
Because Lawful Good, which is supposed to be the epitome of good, or something, tends to create characters who believe the law should rule over people as opposed to the law serving the people.
Lawful Good is NOT the epitome of Good. Good (Lawful, Neutral, or Chaotic) is the epitome of Good by definition.

And the alignment you're describing here is actually Lawful Neutral (getting closer to LE honestly), not Lawful Good. LN characters believe in law over all, whereas LG characters believe in the law to an extent, but not necessarily if it causes more harm than good.

Originally Posted by GM4Him
A Chaotic Good character tends to live in accordance with what's right in spite of whether the law says it's right or not. Thus, they live in more of a way where the law is good, but only if the law is serving the people. When the law becomes abusive, Chaotic Good goes against it because what is more important is the well-being of people.
Again, what you're describing is closer to NG or even LG (your first sentence vs your last 2 sentences, respectively). CG characters in general don't respect any laws, whether they are abusive or not. They reject being constrained by laws.

Originally Posted by GM4Him
But when the law has no such ability to serve the people, the law is not good. Like in the Robin Hood scenario. Therefore, the law creates issues where people must breach it just to survive. Thus, the law is actually evil and people can't live under the burden of it, because there is no provision for which the law can serve. It only dictates and rules.
Yes, laws can be evil. But, as you actually mentioned in your tax-collector example where he gets a waiver for that lady, taxes can also be good. Theoretically these taxes can be used to build roads and fund education or arts. Laws are not evil or good by themselves, just as Lawful characters are not automatically evil or good. It operates on a case-by-case basis.

Originally Posted by GM4Him
Animals don't have, if you notice, evil laws.
Fixed that for you. Animals are neither evil nor good, neither lawful nor chaotic. They act according to their instince. Unless by "laws" you mean "physical laws," but again that's irrelevant to the discussion of D&D Alignment.