En caso de que tengas dudas con el pronombre, pregúntale a la profesora después de clase.

Because en caso de que is normally followed by the subjunctive in Spanish.

Here, the speaker is talking about a possible situation in the future: if you happen to have doubts. Since it is hypothetical or not yet confirmed, Spanish uses tengas.

• En caso de que tengas dudas... = in case you have doubts...
• Tienes would be indicative, and that would sound wrong after en caso de que.

It means in case or if it happens that.

It is a fairly common expression and can sound a little more careful or formal than just si.

Compare:

• En caso de que tengas dudas... = In case you have doubts...
• Si tienes dudas... = If you have doubts...

Both are possible in many contexts, but en caso de que often suggests a precaution: if this situation comes up, do this.

Because en caso de que is the standard fixed expression in Spanish.

The de is part of the structure. So you should learn it as one chunk:

• en caso de que + subjunctive

For example:

• En caso de que llueva...
• En caso de que no puedas venir...

Without a verb, you can also see en caso de:

• En caso de emergencia...
• En caso de duda...

But when a full clause follows, Spanish normally uses de que.

Yes, both can work, but they are slightly different in feel.

• dudas con el pronombre often suggests difficulty with / uncertainty about using it
• dudas sobre el pronombre means questions about the pronoun more generally

In a classroom context, dudas con sounds very natural when talking about trouble with grammar, exercises, or usage.

You will also hear:

• tener dudas sobre algo
• tener dudas con algo

Both are common, but con is especially natural for school-type problems.

Because Spanish often uses the singular to talk about a concept in a general way, or because the speaker may be referring to the pronoun currently being discussed.

So:

• el pronombre = the pronoun / pronouns as a topic / the specific pronoun in question
• los pronombres = pronouns in general, more explicitly plural

If the class is dealing with one specific pronoun, the singular makes perfect sense. If the speaker means pronouns in general, the plural would also be possible in another sentence.

Pregúntale is made of two parts:

• pregunta = the tú affirmative command of preguntar
• le = to her / to him / to you (formal singular)

So:

• pregunta
  • le → pregúntale

In this sentence, le means to her, referring to la profesora.

So the structure is basically:

• pregúntale a la profesora = ask the teacher

Because when the pronoun le is attached to the command, Spanish adds a written accent to keep the original stress.

Without the pronoun:

• pregunta

With the pronoun attached:

• pregúntale

The accent shows that the stress still falls where it should.

This is very common with commands plus attached pronouns:

• dime
• explícamelo
• escríbelo
• pregúntale

Because in Spanish, it is very common to use an indirect object pronoun together with the full noun phrase.

So le and a la profesora both refer to the same person.

This is called clitic doubling, and it is extremely normal in Spanish:

• Le di el libro a Marta.
• Les expliqué la regla a los estudiantes.
• Pregúntale a la profesora.

The pronoun is not optional in standard Spanish here; it is the normal way to say it.

Because preguntar often uses this pattern:

• preguntar algo a alguien = to ask someone something

Even when the something is not stated, the person being asked still appears with a:

• Pregúntale a la profesora.

So here:

• a la profesora = to the teacher

This a is part of how Spanish marks the person involved.

Yes, you may hear that, and it can be understood, but pregúntale a la profesora is more natural and more complete in standard Spanish because the indirect object pronoun le is normally used.

So:

• Pregúntale a la profesora = the most natural version
• Pregunta a la profesora = understandable, but less idiomatic in this kind of sentence

Both mean a female teacher, but they are used a bit differently.

In Spain:

• profesor / profesora is the most common word for a teacher, especially in secondary school, university, and often generally in education
• maestro / maestra is more associated with primary school, though usage can vary

So la profesora sounds very natural here, especially in an academic context.

Después de clase means after class in a general, idiomatic way.

When Spanish leaves out the article here, it often refers to the activity or period as a general event:

• antes de clase
• después de clase

Después de la clase is also possible, but it sounds more specific: after the particular class/lesson.

So:

• después de clase = after class, idiomatic and general
• después de la clase = after that specific class

It is talking to one person informally, using tú.

You can see that in:

• tengas
• pregúntale

The command is a tú command.

If the speaker were addressing someone formally (usted), it would be different:

• En caso de que tenga dudas..., pregúntele a la profesora...

So the original sentence is informal singular.

Yes. Le can mean:

• to him
• to her
• to you (formal singular)

You understand which one it means from the context.

Here, the sentence says a la profesora, so le clearly means to her.

That is why the full phrase helps:

• pregúntale a la profesora = ask the teacher

Without a la profesora, pregúntale by itself could mean ask him, ask her, or ask them? Actually singular le usually means one person, though in some varieties there can be variation. In this sentence, the noun removes any ambiguity.