Learn Hardcore Japanese: sensei ha gakusei ni nihongo wo osiemasu. - The teacher teaches Japanese to students.

は marks the topic of a sentence—what you’re talking about. In 先生は…, the teacher is an established topic.
By contrast, が marks the subject when you’re introducing new information or emphasizing who does the action. If you said 先生が学生に日本語を教えます, it would emphasize “it is the teacher (not someone else) who teaches Japanese to the student.”

Why is に used after 学生? Could we use へ or を instead?

The particle に indicates the indirect object or recipient of the action—in this case, the student who receives the teaching.

へ generally marks physical direction (“to/toward”) and sounds odd here.
を marks the direct object (“what” is being taught), so using 学生を would wrongly treat the student as the thing being taught.

What does を after 日本語 signify?

を marks the direct object of the verb 教えます—it shows what is being taught. So 日本語を教えます means “teaches Japanese.”

Could we rearrange the word order of this sentence?

Japanese word order is flexible for nouns and their particles, but the verb usually comes at the end. You could swap the two objects:

先生は日本語を学生に教えます
Both orders are grammatical and sound natural, though changing the order may slightly shift the focus (first mentioning what is taught vs. who receives it).

Why is the verb in the polite ます form (教えます) and not in the dictionary form (教える)?

教えます is the polite non-past form, suitable for neutral or formal conversation.
教える is the plain (dictionary) form, used in casual speech or writing among friends, in notes, or when quoting dictionaries.

There’s no plural marker after 学生. How do we know if it’s one student or many?

Japanese nouns don’t usually distinguish singular vs. plural. Context tells you whether it’s one student or multiple students. If you want to emphasize plural explicitly, you can say 学生たち (gakusei-tachi) to mean “students.”

Can we drop the topic 先生は if the context is clear?

Yes. Japanese often omits the topic when it’s understood. For example, in a classroom you might simply say 学生に日本語を教えます to mean “(I/We) teach Japanese to students,” relying on context for who is doing the teaching.

Why is は pronounced wa here and not ha?

When the hiragana は functions as the topic particle, it’s always pronounced wa, even though in other words (like はな “hana” flower) it’s pronounced ha.