Learn Hardcore Spanish (Latin America): La maestra de yoga corrige mi postura y me enseña a relajar los hombros. - The yoga teacher corrects my posture and teaches me to relax my shoulders.

In Spanish, you almost never put a noun directly in front of another noun as in yoga teacher.
Instead, you say [profession/role] + de + [activity/field]:

maestra de yoga = yoga teacher
profesor de matemáticas = math teacher
entrenador de fútbol = soccer coach

So la maestra de yoga is the natural way to say the yoga teacher.
A phrase like la yoga maestra sounds wrong in modern Spanish.

What is the difference between maestra, profesora, instructora, or entrenadora for a yoga teacher?

All of these can appear with de yoga, but the nuance changes a bit:

maestra de yoga – literally yoga teacher. In Latin America, maestra often evokes a schoolteacher (especially for children), but some people do use mi maestra de yoga to mean their yoga teacher, especially in more personal or spiritual contexts.
profesora de yoga – also yoga teacher, a bit more academic or formal sounding; very common.
instructora de yoga – yoga instructor, slightly more technical / practical.
entrenadora de yoga – yoga trainer/coach; less common, but possible if you think of yoga as a physical training activity.

All are understandable; profesora de yoga and instructora de yoga are probably the most neutral choices.

Why is it corrige mi postura but me enseña a relajar los hombros? Why not me corrige la postura too?

Both patterns are possible:

corrige mi postura – uses the possessive mi (my posture).
me corrige la postura – uses an indirect object pronoun me plus a definite article la (she corrects the posture for me / of me).

In everyday Spanish, me corrige la postura is very common and actually sounds a bit more natural than corrige mi postura.
Your sentence is correct as written, but another very natural version would be:

La maestra de yoga me corrige la postura y me enseña a relajar los hombros.

Both verbs are then clearly acting on me.

Why do we need me in me enseña a relajar los hombros? Could I just say enseña a relajar los hombros?

me is an indirect object pronoun that tells you who is being taught:

me enseña a relajar los hombros = she teaches me to relax my shoulders.

If you remove it:

enseña a relajar los hombros = she teaches (people in general) to relax their shoulders / she teaches how to relax the shoulders.

Both are grammatically fine, but the meaning changes.
If you want to say she teaches me specifically, you need the me.

Why is it enseñar a + infinitive in me enseña a relajar? Can I say me enseña relajar without a?

With enseñar meaning to teach someone to do something, Spanish normally uses:

enseñar a + infinitive

Examples:

Me enseñó a manejar. = She taught me to drive.
Nos enseñan a respirar bien. = They teach us to breathe correctly.

So me enseña a relajar los hombros follows this pattern.
Me enseña relajar los hombros (without a) sounds incorrect or at least very unnatural.

Why is it a relajar los hombros (non‑reflexive), and not a relajarme los hombros or a relajarme?

relajar is a transitive verb here: you relax something (your shoulders):

relajar los hombros = to relax the shoulders.

You normally don’t say relajarme los hombros in Spanish.
Instead, Spanish uses either:

relajar + body part: relajar los hombros, relajar la espalda.
or a general reflexive: relajarse = to relax (oneself) in general, not a specific body part.

So you’d say:

Me enseña a relajar los hombros. (specific body part)
Me enseña a relajarme. (to relax myself / to calm down)

Mixing both (a relajarme los hombros) is not natural.

Why is it los hombros and not mis hombros if we mean my shoulders?

Spanish often uses the definite article with body parts and a pronoun for the person:

Me duele la cabeza. = My head hurts.
Me lavo las manos. = I wash my hands.

So (me enseña a) relajar los hombros is understood as relax my shoulders from the context (me).
You can say mis hombros (a relajar mis hombros), and it is grammatically correct, but with this kind of verb and body part, los hombros is more natural.

Why is it La maestra de yoga corrige mi postura y me enseña… and not …corrige mi postura y enseña… without the second subject?

In Spanish, once you have a clear subject (la maestra de yoga), you don’t need to repeat it with each verb.

The subject la maestra de yoga applies to both verbs:

(La maestra de yoga) corrige mi postura y (la maestra de yoga) me enseña a relajar los hombros.

You can omit it the second time because the verb endings (corrige, enseña) already show third person singular and the context is clear.
If you dropped me as well (…y enseña a relajar los hombros), it would still refer to her, but you would lose the idea of teaches me.

Is there any difference between postura and posición here? Could I say corrige mi posición?

Both postura and posición can refer to how your body is placed, but:

In yoga, exercise, dance, etc., postura is more common and sounds more technical/natural.
posición is more general (position, place) and is fine, but less idiomatic in a yoga context.

So:

corrige mi postura = she corrects my posture / pose (very natural for yoga).
corrige mi posición = understandable, but feels more neutral or less tied specifically to yoga jargon.

Why is corrige in the simple present? Does it mean she is doing it right now or that she usually does it?

Spanish simple present (corrige, enseña) can express:

An action happening now:
- (Ahora mismo) corrige mi postura. = Right now, she is correcting my posture.
A habitual action:
- Siempre corrige mi postura. = She always corrects my posture.

Without extra context, your sentence can be understood either way.
If you really want to emphasize “right now,” you can use the progressive:

La maestra de yoga está corrigiendo mi postura y me está enseñando a relajar los hombros.

But the simple present is very natural even for current actions in Spanish.

Why isn’t there a personal a before mi postura in corrige mi postura?

The personal a is used before a direct object that is usually:

a person,
a beloved animal,
or sometimes a personified thing.

Here, mi postura is a thing (my posture), not a person, so you do not use a:

corrige mi postura – correct.
corrige a mi postura – incorrect in this meaning.

You would use a with people:

Corrige a los alumnos. = She corrects the students.

Could I change the word order of the pronoun and say enseña me a relajar los hombros?

No. With a simple conjugated verb in Spanish, unstressed pronouns like me must go before the verb:

me enseña – correct.
enseña me – incorrect (except in very old or poetic Spanish).

The pronoun can go after the verb only if the verb is in infinitive, gerund, or affirmative command:

enseñarme a relajar los hombros (infinitive)
está enseñándome a relajar los hombros (gerund)
Enséñame a relajar los hombros. (command)

In your sentence, me enseña is the only correct order.

How would I say my yoga teacher instead of the yoga teacher in this sentence?

You simply add the possessive:

Mi maestra de yoga corrige mi postura y me enseña a relajar los hombros.

The rest of the sentence stays the same.
You could also choose another noun if you prefer:

Mi profesora de yoga corrige mi postura y me enseña a relajar los hombros.
Mi instructora de yoga corrige mi postura y me enseña a relajar los hombros.

All of these are natural ways to say my yoga teacher in Latin American Spanish.