Learn Hardcore Spanish (Latin America): Voy acumulando errores en la lección cuando hablo rápido. - I keep accumulating mistakes in the lesson when I speak fast.

Acumulo errores would mean something like “I (generally) accumulate errors” – a simple, habitual statement.
Voy acumulando errores adds the idea of gradual accumulation over time: I keep building up errors / I go on accumulating errors.
That voy (from ir) suggests a process that progresses little by little, not just a static habit.

What grammar structure is voy acumulando? How is it different from normal present or future?

Voy acumulando is ir + gerund (in this case, ir in the present: voy).
In Spanish, ir + gerund often means “to gradually keep doing something”.
It is not the same as voy a acumular (which is a periphrastic future: I’m going to accumulate), and it’s a bit more nuanced than acumulo (plain present) or estoy acumulando (action in progress right now).
Here it suggests: As I speak fast, the errors pile up more and more.

Could I say Estoy acumulando errores en la lección instead? What’s the difference?

Yes, Estoy acumulando errores en la lección is grammatically correct.
However, estoy acumulando focuses on what’s happening right now (I am in the process of accumulating errors).
Voy acumulando emphasizes the gradual build‑up over time or over the course of the activity, which fits very well with cuando hablo rápido (whenever I speak fast → they start to pile up).
Both are understandable, but voy acumulando sounds more like “they keep adding up.”

Could I say Voy a acumular errores en la lección? Does that mean the same thing?

No, it doesn’t mean the same thing.
Voy a acumular errores is future: I’m going to accumulate errors (I will accumulate them), almost like an intention or prediction.
Voy acumulando errores describes what tends to happen as the situation develops, not what will happen in the future.
So in this context, voy a acumular would sound odd or unintended.

Why is it cuando hablo rápido and not cuando estoy hablando rápido?

Spanish normally uses the simple present for general, habitual situations, where English often uses “when I’m doing X”.
Cuando hablo rápido = when(ever) I speak fast (in general).
Cuando estoy hablando rápido would sound more like at the specific moment when I happen to be speaking fast, and is less natural for a general tendency.
So the simple present hablo is the normal choice here.

Why is hablo in the indicative and not hable (subjunctive) after cuando?

Cuando + indicative is used for real, habitual, or completed actions: Cuando hablo rápido, cometo errores = Whenever I speak fast, I make mistakes.
Cuando + subjunctive (cuando hable) is used mainly for future or uncertain events: Cuando hable con el profesor, le preguntaré = When I speak with the teacher (in the future), I’ll ask him.
In this sentence, you’re describing a general, repeated situation, so cuando hablo rápido with the indicative is correct.

Could I say cometo errores instead of acumulo errores? Is there any difference?

Yes, you absolutely can say Voy cometiendo errores en la lección cuando hablo rápido.
Cometer errores is the most standard collocation for “to make mistakes” (better than hacer errores, which sounds wrong or foreign).
Acumular errores adds a nuance: it imagines the errors as piling up, one on top of another.
So cometer = make errors; acumular = end up with more and more errors collected.

Is hago errores acceptable, like “I make errors” in English?

No, hago errores is not idiomatic Spanish.
The natural expression is cometer errores.
So you’d say Cometo muchos errores cuando hablo rápido, not Hago muchos errores.
In your original sentence, acumular errores is also fine and adds the idea of them piling up.

Why is it en la lección? Could I say en la clase instead? Is there a difference?

Both en la lección and en la clase can be correct, but they feel slightly different.

Lección usually refers to a specific lesson or unit of content (like Lesson 3 in a textbook, or a particular online lesson).
Clase often refers to the class session or the physical/virtual class you attend.

In much of Latin America, en la clase is very common when talking about what happens during class time.
So if you mean “in this lesson (unit) of my course,” en la lección is fine; if you mean “during class,” en la clase may sound more natural.

Could I move rápido earlier, like cuando rápido hablo, or put it somewhere else?

No, cuando rápido hablo is not natural Spanish.
The normal word order is cuando hablo rápido (verb + adverb), just like cuando hablo despacio or cuando hablo bien.
You can add intensifiers, e.g. cuando hablo muy rápido or cuando hablo demasiado rápido, but rápido still comes after hablo.

Is rápido an adjective or an adverb here? Could I use rápidamente instead?

Here rápido functions as an adverb (describing how you speak).
In Spanish, many adjectives can be used adverbially in this way, especially rápido, lento, fuerte, claro, etc.
You could say cuando hablo rápidamente, and it’s grammatically correct, but in everyday Latin American Spanish rápido sounds more natural and conversational.
Rápidamente is a bit more formal or bookish in many contexts.

Could I say Yo voy acumulando errores? Is adding yo wrong or different?

Adding yo is not wrong; it’s perfectly grammatical: Yo voy acumulando errores en la lección cuando hablo rápido.
However, in Spanish the subject is usually clear from the verb ending (voy = first person singular), so yo is often dropped.
You typically include yo only for emphasis or contrast, e.g. Yo voy acumulando errores, pero mis compañeros no (I keep accumulating errors, but my classmates don’t).
Without that contrast, the shorter version without yo sounds more natural.

Is the sentence natural in Latin American Spanish, or would a native say it differently?

The sentence is perfectly understandable and acceptable in Latin American Spanish.
Some speakers might more spontaneously say things like:

Voy cometiendo errores en la clase cuando hablo rápido.
Cuando hablo rápido, voy acumulando muchos errores.

But your original Voy acumulando errores en la lección cuando hablo rápido is grammatically correct and sounds fine, especially in the context of a course or textbook “lesson.”