Learn Finnish: Hän ei opi nopeasti. - He does not learn fast.

The dictionary form of the verb is oppia (to learn). When making a negative sentence for a Type 1 verb, you drop the personal ending to get the negative stem, and use its weak grade. This means the strong double pp weakens to a single p, giving us opi.

Does the verb opi change if I say "I do not learn" instead of "he does not learn"?

No, the main verb stem (opi) stays exactly the same! In Finnish negative sentences, it is the negative word that changes to match the person. "I do not learn" is en opi, while "he does not learn" is hän ei opi.

How is the word nopeasti (fast/quickly) formed?

The basic adjective for "fast" or "quick" is nopea. In Finnish, you can usually turn an adjective into an adverb (a word that describes how an action is done) by adding the ending -sti. It works just like adding "-ly" in English!

Does hän specifically mean "he"?

Hän means both "he" and "she". Finnish pronouns do not have gender, so you use the exact same word for everyone. The translation says "he" here, but it could just as easily be translated as "she" depending on the context of the conversation.