No quiero posponer la cita con la dentista otra vez, porque luego nunca encuentro hueco.

Here, cita means appointment.

In Spanish, cita can mean either date or appointment, so the context matters. Because the sentence says con la dentista, it clearly means a medical appointment.

• Tengo una cita con alguien could be a date or an appointment, depending on context.
• Tengo cita con la dentista is clearly an appointment.

Because after querer, Spanish normally uses an infinitive when the subject stays the same.

So:

• No quiero posponer... = I do not want to postpone...
• same subject: I do not want to postpone

If the subject changes, Spanish usually uses querer que + subjunctive:

• Quiero que vengas = I want you to come

But in your sentence, the same person is doing both actions, so querer + infinitive is the normal structure.

Yes. Aplazar and posponer are both good translations of to postpone.

There is a slight difference in feel:

• posponer = postpone, put off until later
• aplazar = postpone, delay, often very common for appointments, meetings, exams, etc.

So these both sound natural:

• No quiero posponer la cita...
• No quiero aplazar la cita...

In everyday Spanish from Spain, both are fine here.

Because Spanish usually says cita con + person when you mean an appointment with someone.

So:

• Tengo cita con la dentista = I have an appointment with the dentist

By contrast, para is often used for time, purpose, or destination:

• Tengo cita para el martes = I have an appointment for Tuesday
• Tengo cita para una revisión = I have an appointment for a check-up

So in your sentence, con la dentista is the most natural way to express with the dentist.

Dentista is one of those nouns that often has the same form for both masculine and feminine. The article tells you the gender of the person.

• el dentista = the male dentist
• la dentista = the female dentist

This is common with many profession words ending in -ista:

• el artista / la artista
• el periodista / la periodista

So la dentista simply tells you the dentist is a woman.

Otra vez means again.

So:

• posponer la cita otra vez = postpone the appointment again

It refers to repeating the action of postponing.

You could also say:

• No quiero volver a posponer la cita...

That is also very natural and means almost the same thing.

In many cases, otra vez, de nuevo, and volver a + infinitive can all express again, though otra vez is very common in everyday speech.

Yes, Spanish often allows some flexibility with adverb placement.

These are all possible:

• No quiero posponer la cita con la dentista otra vez
• No quiero volver a posponer la cita con la dentista
• No quiero otra vez posponer la cita con la dentista — possible, but less natural

The original version sounds very normal. Putting otra vez near the end is a common way to place again in Spanish.

Here, luego means later, afterward, or then.

So:

• porque luego nunca encuentro hueco = because afterward I never find an opening / a free slot

In Spain, luego is very common in everyday speech for later or then.

Literally, hueco means gap, space, or hole. But in this context, it means a free slot or opening in a schedule.

So:

• encontrar hueco = find room in the schedule
• no tengo hueco = I do not have any free time / any availability

This is very common in Spain when talking about appointments, calendars, and busy schedules.

Both are possible.

• encontrar hueco = find availability, find room in the schedule
• encontrar un hueco = find a free slot, one opening

Without the article, it sounds a bit more general and idiomatic. It is like saying find room rather than find a slot.

So the sentence sounds very natural as written, but porque luego nunca encuentro un hueco would also be possible.

Because encontrar is a stem-changing verb in the present tense.

The o changes to ue when the syllable is stressed:

• encuentro
• encuentras
• encuentra
• encuentran

But not in:

• encontramos
• encontráis

This is a very common pattern in Spanish, like:

• poder → puedo
• volver → vuelvo

So encuentro is the correct first-person singular present form.

Because Spanish often uses the present tense for things that are habitual or generally true.

Here, the meaning is something like:

• whenever I postpone it, later I never manage to find a free slot

So nunca encuentro hueco expresses a repeated pattern, not just one future event.

If you wanted to make it sound more like a prediction about this specific case, you could say something like:

• porque luego no voy a encontrar hueco
• porque luego no encontraré hueco

But the present tense in the original sentence sounds very natural.

Because nunca comes before the verb.

In Spanish, if a negative word such as nunca, nadie, or nada comes before the verb, you usually do not add no:

• Nunca encuentro hueco
• Nadie vino
• Nada funciona

If the negative word comes after the verb, then you normally use no as well:

• No encuentro nunca hueco

So in your sentence, luego nunca encuentro hueco is correct because nunca is placed before encuentro.

Yes, absolutely. That is very natural.

• No quiero posponer la cita con la dentista otra vez
• No quiero volver a posponer la cita con la dentista

Both mean basically the same thing.

The second version may even sound slightly more idiomatic to some speakers, but the original sentence is completely natural too.