Learn Russian: Наконец я понял правило.

Even though this is a past tense verb rather than an infinitive, the core rule of aspect still applies: perfective verbs focus on the result. The speaker successfully completed the action and grasped the concept. If they used the imperfective понимал, it would mean they were in the ongoing process of understanding it without reaching a final conclusion.

How do we know if a man or a woman is saying this sentence?

We know it is a man because the past tense verb понял ends in -л, which is the masculine ending. If a woman were saying this, she would use the feminine past tense form and say поняла.

Why doesn't the word правило change its ending here?

The word правило is the direct object of the sentence (it is the thing being understood), so it must be in the accusative case. However, for neuter inanimate nouns like правило, the accusative form looks exactly the same as the basic dictionary form.

Is the word Наконец related to the Russian word for end?

Yes! It contains the root конец, which means end. So наконец is built to mean on the end, which is why it translates to finally or at last.