Learn Hardcore German: Ich komme pünktlich zum Unterricht.

The adverb pünktlich and the situation (a scheduled class) show that this is about the future.
Using werden here (Ich werde pünktlich zum Unterricht kommen.) is also correct, but it’s usually only needed to emphasize or clarify the future, or in more formal/explicit style. In everyday speech the simple present is completely normal.

Why is it komme and not gehe? In English I’d usually say “I’m going to class,” not “I’m coming to class.”

Both kommen and gehen can be possible, but they focus on different perspectives:

Ich komme pünktlich zum Unterricht.
→ I (will) arrive on time for class.
Focus: moving towards the place or event where the listener or group already is or will be. You’re joining them.
Ich gehe pünktlich zum Unterricht.
→ I (will) go to class on time.
Focus: your movement away from where you are now towards the class.

In many contexts, kommen is used when you’re talking to someone who will also be at the class (teacher, classmate), as if you’re saying “I’ll come to you/your event on time.”

What exactly does pünktlich mean? Is it the same as “on time”? Could I say rechtzeitig instead?

pünktlich = exactly at the agreed time, neither late nor noticeably early.
It’s very close to “on time / punctual”.

Ich komme pünktlich zum Unterricht.
→ You arrive right when class is supposed to start.

rechtzeitig = early enough, “in time,” with a bit more flexibility.

Ich komme rechtzeitig zum Unterricht.
→ You won’t be late, but you might be slightly early; it just means you arrive before it’s too late.

Both are correct, but pünktlich emphasizes the exact time, rechtzeitig emphasizes not being too late.

Why is it zum Unterricht and not zu dem Unterricht?

zum is simply the contraction of zu dem:

zu
- dem → zum

So:

Ich komme pünktlich zu dem Unterricht. (formal/spelled out)
Ich komme pünktlich zum Unterricht. (normal, preferred in speech and writing)

They mean the same thing; zum is just the standard contracted form.

Why is zum Unterricht dative? Could it be accusative, like zu den Unterricht?

The preposition zu always takes the dative case.

The noun Unterricht is masculine:

Nominative: der Unterricht
Accusative: den Unterricht
Dative: dem Unterricht

Since zu requires dative, you must use dem:

zu dem Unterricht → zum Unterricht

zu den Unterricht would be wrong for two reasons:

zu needs dative, not accusative (dem, not den), and
den Unterricht is singular accusative, which zu never takes.

What’s the difference between Unterricht, Kurs, and Klasse? Why is it Unterricht here?

They overlap, but they’re not the same:

der Unterricht
= instruction / teaching / lesson(s) as an activity.
- Ich habe heute Deutschunterricht. – I have German class today.
  In zum Unterricht you’re talking about the teaching session in general.
der Kurs
= course, a structured series of lessons (language course, yoga course, etc.)
- Ich mache einen Deutschkurs. – I’m taking a German course.
die Klasse
1. A group of pupils in school:
  - Meine Klasse ist laut. – My class (group of students) is loud.
2. Sometimes the school year level:
  - Ich bin in der 8. Klasse.

In Ich komme pünktlich zum Unterricht, the focus is on the teaching session / lesson you are attending, so Unterricht is the natural choice.

Why is pünktlich before zum Unterricht? Can I say Ich komme zum Unterricht pünktlich?

Neutral word order in German usually places short adverbs before longer prepositional phrases, especially with time and place elements:

Ich komme pünktlich zum Unterricht.
(adverb pünktlich → then prepositional phrase zum Unterricht)

You can say:

Ich komme zum Unterricht pünktlich.

This is grammatically correct, but it sounds more marked/emphatic, as if you were stressing pünktlich (maybe in contrast: “I may not be well prepared, but I will be on time”).

For a simple, neutral statement, Ich komme pünktlich zum Unterricht is the standard word order.

What’s the difference between zum Unterricht and in den Unterricht?

Both can appear in similar contexts but with a nuance:

zum Unterricht (using zu
- dative)
  → going to the lesson as an event or appointment.
  Focus: attending/being present.
- Ich komme pünktlich zum Unterricht. – I (will) come on time for class.
in den Unterricht (using in
- accusative)
  → going into the lesson / classroom.
  Focus: physical movement into the space.
- Ich gehe jetzt in den Unterricht. – I’m going into class now.

In your sentence, the important part is that you attend/be there on time, so zum Unterricht is the most natural.

Is Unterricht countable? Why don’t we say something like zu dem Unterrichtsstunde?

Unterricht is usually treated as uncountable in German when you mean “instruction” or “class” in general:

Ich habe heute drei Stunden Unterricht.
– I have three hours of class today.

If you want to count individual lessons, you typically use die Stunde (lesson/hour):

eine Stunde Deutschunterricht – one hour of German class.

You wouldn’t normally say Unterrichtsstunde in everyday speech here. It exists, but it’s more formal/technical (used in school administration, timetables, etc.).
So zum Unterricht is the natural, idiomatic way to say “to class.”

How are ich, pünktlich, and Unterricht pronounced? Especially the ü and the ch?

Key points:

ich
- i like in English “bit” (but shorter/tenser).
- ch = soft ich-sound, made by raising the middle of your tongue towards the hard palate (similar to hissing air gently), not like English “k” or “sh.”
pünktlich
- ü is like saying English “ee” (as in “see”) but with rounded lips.
- pünk-: the ü is short; -kt- cluster is pronounced clearly.
- The final -lich again has that soft ich-sound for ch.
Unterricht
- Stress on the first syllable: UN-ter-richt.
- Final -richt also has the same soft ch sound as in ich.

So the ch in all three words is the same soft sound (the ich-Laut), not the harsher ach-Laut you hear in Bach or auch.