Learn German: Man lernt die Aussprache effektiv, indem man gut zuhört. - You learn the pronunciation effectively by listening well.

indem is a subordinating conjunction that means "by doing something". It tells us the method used to achieve the action in the main clause. Like other subordinating conjunctions (such as weil or dass), it kicks the conjugated verb to the very end of its clause: indem man gut zuhört.

Why isn't the separable prefix of zuhört split from the verb here?

The verb is zuhören (to listen). Normally in a main clause, you would split it: Man hört gut zu. However, because indem is a subordinating conjunction, it sends the conjugated verb to the end of the clause. When a separable verb is pushed to the end like this, the prefix and the verb reattach and are written as one single word: zuhört.

Do we have to repeat man in the second part of the sentence?

Yes. In English, you can simply say "You learn... by listening", dropping the second "you". In German, an indem clause is a full subordinate clause, which means it requires its own subject. Since the subject is the general man (one/you) in the first half, we must state it again in the second half.

What is the difference between zuhören and just hören here?