La profesora me dijo que tenía un hueco después del seminario.

Spanish uses articles more often than English. Here la profesora means the teacher / the female teacher, referring to a specific person.

You usually drop the article with professions only in certain structures, especially after ser:

• Es profesora = She is a teacher

But when you are talking about a particular person, la profesora is normal.

Me is the indirect object pronoun, meaning to me.

The basic pattern is:

• decir algo a alguien = to tell something to someone

So:

• La profesora me dijo... = The teacher told me...

If you remove me, the sentence just means The teacher said..., without saying who she said it to.

Because the act of telling is seen as one completed event in the past.

• dijo = she told / said
• decía would suggest something ongoing, repeated, or backgrounded, like she was saying or she used to say

In this sentence, the speaker is referring to one specific moment when the teacher said it, so dijo fits best.

Here que introduces the reported statement, just like that in English:

• me dijo que... = told me that...

In English, that is often optional. In Spanish, que is usually required after decir in this kind of sentence. Leaving it out would sound unnatural or wrong here.

Tenía is imperfect because it describes a state or situation in the past: the teacher had some free time available.

It also matches normal reported speech after a past reporting verb:

• direct speech: Tengo un hueco después del seminario
• reported speech: Me dijo que tenía un hueco después del seminario

Why not the others?

• tiene would keep it in the present, which is possible only if the speaker wants to present the information as still true now
• tuvo sounds like a completed, bounded event, which is less natural for this idea of availability

Normally, the most natural interpretation is that tenía refers to la profesora.

So the usual meaning is:

• the teacher told me that she had a free slot after the seminar

Spanish often leaves subjects unstated when they are clear from context. If you wanted extra clarity or emphasis, you could say ella tenía, but in most cases that is unnecessary.

In Spain, tener un hueco is a very common everyday expression meaning to have:

• a free slot
• some free time
• an opening in your schedule

Literally, hueco can mean gap, space, or hole, but here it is idiomatic. It does not mean a physical hole.

Because de + el contracts to del in standard Spanish.

So:

• después de el seminario is not correct
• después del seminario is correct

This contraction is normally mandatory. A well-known exception is when El is part of a proper name, such as de El Escorial.

Yes. Some natural alternatives are:

• La profesora me dijo que estaba libre después del seminario.
• La profesora me dijo que tenía tiempo después del seminario.
• Me dijo la profesora que tenía un hueco después del seminario.

The original sentence sounds very natural in Spain, especially because tener un hueco is such a common expression there.