What if it's a stupid rule, like no passing erasers during a test? or a stupid law, like not having a donkey in a bathtub?

For every rule, there's someone who thinks it's a stupid rule. That goes for rules like no murder, no rape and no assault. Does the person who trangresses the rule the person who gets to determine if the rule is stupid?

If it's society who gets to decide, they already did. They made the rule. If and when society decides that the rule is stupid, they would collectively vote or decide to change it.

As for the no passing eraser rule, if there was such a rule and she broke it, then she wouldn't have a right to complain about it. The reason she's complaining about it was because the rule was no cheating and she didn't think that passing the eraser qualified under that rule since she knew she wasn't cheating. That was a case of administration of the rule, not the rule itself. There will always be errors in administration of rules because intent is not 100% ascertainable. In this case, the teacher believed her and let her take the test again. She wasn't penalized because the teacher believed it was not her intent to cheat.

In the words of Heinlein,

That's a quote from a piece of science fiction that is about hypothesizing about different moral systems on another planet. I don't see any evidence from the wiki that Heinlein himself lived by that philosophy or even believed in it. Is there more evidence that he behaved according to this philosophy in his real life?

What I'm really asking is, should we believe in Rule Ethics (Deontology or Rule Consequentialism)?

In this case, there isn't a need to decide. Both apply. There's a rule that was broken. (deontology in your parlance) If everyone broke the rule of cheating on exams, then tests would become meaningless. (consequentialism in your terms)

In the wiki, it says that deontological ethics are often contrasted with virtue ethics and pragmatic ethics as well. As to virtue ethics, again there's no need to decide unless you decide there's virtue in cheating.

Pragmatic ethics doesn't really apply here. The social convention of taking tests and measuring achievement based on them is the foundation for the example of cheating in the article.

If something is otherwise right, but breaks a law, is it wrong? Is it wrong to steal an apple to feed a starving child? Is it wrong to change lanes while driving without signalling, when someone is about to hit you and you don't have time to think?

These don't apply to the article. These are all example of two conflicting morals.

The woman who is cheating on tests isn't saving a life or creating a moral good or even preventing a bad thing by cheating. She's just giving in to social pressure to cheat.

When there are two conflicting morals at play, there are decisions to be made in weighing which one takes precedence in the given moment. In this case, there's no such conflict.