Ya sea por la mañana o por la tarde, necesito un hueco para llevar el justificante al ayuntamiento.

It means whether it be ... or ..., or more naturally in English, whether ... or ....

So Ya sea por la mañana o por la tarde means something like Whether in the morning or in the afternoon. It introduces two possible options without choosing one yet.

This structure is very common in Spanish:

• ya sea café o té = whether coffee or tea
• ya sea hoy o mañana = whether today or tomorrow

Sea is the present subjunctive of ser.

In the fixed expression ya sea ... o ..., Spanish uses the subjunctive because the speaker is presenting alternatives or possibilities, not stating one definite fact. For a learner, it is best to treat ya sea ... o ... as a chunk you can memorize.

So:

• es = indicative, used for direct statements
• sea = subjunctive, used here in this set expression of alternatives

Because in Spanish, especially in Spain, por la mañana, por la tarde, and por la noche are the normal expressions for in the morning, in the afternoon/evening, and at night.

Here por is just part of the standard time expression. It does not translate word-for-word very neatly.

In Spain:

• por la mañana is much more natural than en la mañana
• por la tarde is the usual way to say in the afternoon

Literally, hueco can mean gap, space, or hole. But in this sentence, un hueco means a free slot, a bit of free time, or an opening in my schedule.

This is a very common expression in Spain:

• Tengo un hueco a las cuatro = I have a free slot at four
• Necesito un hueco = I need to find some time

So it is not a physical hole here. It is a time gap in someone's schedule.

Because para + infinitive is a very common way to express purpose in Spanish.

So:

• necesito un hueco = I need some free time
• para llevar el justificante al ayuntamiento = in order to take the document to the town hall

In other words, para llevar explains why the speaker needs that free slot.

This is very natural Spanish:

• Necesito dinero para viajar = I need money to travel
• Busco tiempo para estudiar = I’m looking for time to study

In Spain, justificante is a common administrative or formal word for a document that proves or supports something.

Depending on context, it could mean:

• a receipt
• a proof of payment
• a supporting document
• a medical note
• a certificate of attendance
• a justification note

So the exact English translation depends on the situation, but the general idea is a document that serves as proof.

Ayuntamiento means town hall, city hall, or sometimes local council, especially in Spain.

Al is the contraction of a + el:

• a el ayuntamiento becomes al ayuntamiento

This contraction is mandatory in normal Spanish.

So:

• llevar el justificante al ayuntamiento = to take the document to the town hall

Because Spanish distinguishes between taking something somewhere and bringing something toward the speaker or listener.

• llevar = to take
• traer = to bring

Since the speaker is talking about taking the document to the town hall, llevar is the natural choice.

Compare:

• Voy a llevar el documento al ayuntamiento = I’m going to take the document to the town hall
• Voy a traer el documento a la oficina = I’m going to bring the document to the office

Yes, but it would sound a bit different.

• Necesito tiempo = I need time
  This is broader and more general.
• Necesito un hueco = I need a free slot / I need to find an opening
  This sounds more specifically like fitting something into a busy schedule.

In everyday Spanish from Spain, un hueco is very natural in this sentence.

Yes. Spanish word order is flexible enough that this phrase can often be moved.

For example:

• Ya sea por la mañana o por la tarde, necesito un hueco...
• Necesito un hueco, ya sea por la mañana o por la tarde...

Putting it first gives it a slightly more framing or introductory feel, as if the speaker is saying whichever of those times it is, I need to make room for this.

So the version in your sentence is perfectly natural.