Vamos a esperar a que deje de llover antes de salir.

Both are possible, but vamos a + infinitive is very common in everyday Spanish for a future plan or intention.

• vamos a esperar = a very natural spoken way to say that we are going to wait
• esperaremos = simple future, also correct, but often sounds a bit more formal, more neutral in writing, or less immediate

So this sentence sounds very natural in conversation.

Because when esperar means to wait for something to happen, Spanish normally uses a que + clause.

So:

• esperar a que deje de llover = to wait for it to stop raining

This a is important. English speakers often want to say esperar que, but that usually means something more like to hope that, not to wait for.

Compare:

• Espero que deje de llover. = I hope it stops raining.
• Espero a que deje de llover. = I’m waiting for it to stop raining.

So in your sentence, a que is required because the idea is waiting for an event.

Because after esperar a que, Spanish uses the subjunctive when the action has not happened yet and is being awaited.

Here, the rain has not stopped yet. It is a future or pending event, so Spanish uses:

• deje = present subjunctive

Not:

• deja = present indicative

So:

• a que deje de llover = waiting for it to stop raining

This is a very common pattern:

• Esperamos a que llegue Ana.
• Voy a esperar a que termine.
• Esperad a que se enfríe.

In all of these, the thing being awaited is still in the future, so the subjunctive is used.

Dejar de + infinitive means to stop + -ing or to stop doing something.

So:

• dejar de llover = to stop raining

Here dejar does not mean to leave or to let. It is part of the fixed expression dejar de.

More examples:

• dejar de fumar = to stop smoking
• dejar de hablar = to stop talking
• dejar de correr = to stop running

So que deje de llover means that it stop raining.

Deje is the present subjunctive, third person singular, of dejar.

It comes from the verb:

• dejar = to stop / to leave / to let

Subjunctive forms:

• yo deje
• tú dejes
• él/ella/usted deje
• nosotros dejemos
• vosotros dejéis
• ellos/ellas/ustedes dejen

In this sentence, deje is third person singular because it is linked to the impersonal idea of rain stopping.

Because Spanish does not need a dummy subject like English it with weather verbs.

In English, we say:

• it is raining
• it stopped raining

But in Spanish, weather verbs are usually used without an expressed subject:

• llueve
• dejó de llover
• deje de llover

So there is no separate word for it here. Spanish simply says the equivalent of stops raining.

Because when the subject is the same in both actions, Spanish usually prefers:

• antes de + infinitive

Here, the implied subject of salir is the same we as in vamos a esperar, so salir is used.

So:

• Vamos a esperar... antes de salir.
  = We will wait... before going out / before leaving.

If the subject were different, you would usually need:

• antes de que + subjunctive

For example:

• Vamos a esperar antes de que ellos salgan.
• Cierra la puerta antes de que entre el gato.

So the infinitive salir is used because the same people who are waiting are also the ones going out.

The subject is understood from the main verb: nosotros.

So the sentence means that we are going to wait, and we are going to go out later.

In Spanish, infinitives do not show person, so the subject is often understood from context.

Here:

• vamos a esperar → subject = we
• antes de salir → understood subject = we

If you wanted a different subject, Spanish would normally use a full clause instead:

• antes de que Ana salga
• antes de que los niños salgan

Yes, hasta que can also appear in this kind of context, but it is a different structure.

• hasta que = until
• a que after esperar = part of the verb pattern esperar a que

So the most direct structure after esperar is:

• Vamos a esperar a que deje de llover.

A very natural alternative is to change the sentence structure:

• No vamos a salir hasta que deje de llover.

That means We’re not going out until it stops raining.

You may also hear:

• Vamos a esperar hasta que deje de llover.

This is understandable and used by many speakers, but for learners, the safest pattern to remember with esperar is:

• esperar a que + subjunctive

Yes. Spanish word order is fairly flexible here.

For example, these are all natural:

• Vamos a esperar a que deje de llover antes de salir.
• Antes de salir, vamos a esperar a que deje de llover.

The basic meaning stays the same. The original order is completely normal and natural.