Me pone nervioso llegar con retraso a una entrevista.

Me is an indirect object pronoun meaning to me.
The structure is algo me pone + adjective, literally something puts me nervous = something makes me nervous.

So:

• Me pone nervioso... = It makes me nervous...
• The thing that causes the feeling is llegar con retraso a una entrevista.

Because the subject of pone is the whole infinitive phrase:

llegar con retraso a una entrevista

That entire action is treated as one thing, so Spanish uses third person singular:

• Me pone nervioso llegar... = Arriving... makes me nervous
• Compare: Me gusta leer = Reading pleases me / I like reading

Spanish often uses the infinitive to talk about an action in a general way, like English arriving, being late, speaking in public, etc.

So:

• llegar con retraso = to arrive late / arriving late

It is not llego because that would mean I arrive as a fully conjugated verb, and it is not acting as the subject in the same way.

It is not llegando because the gerund in Spanish is used much less freely than English -ing forms. In this sentence, the natural form is the infinitive.

The adjective agrees with the person who feels nervous, not with the action.

Here, nervioso describes the speaker, represented by me.

So:

• a male speaker would usually say Me pone nervioso...
• a female speaker would usually say Me pone nerviosa...

The adjective does not agree with entrevista or with llegar.

Poner nervioso means to make someone nervous.

It is a very common Spanish pattern:

• Me pone nervioso = It makes me nervous
• Te pone nervioso = It makes you nervous
• Nos pone nerviosos = It makes us nervous

It is often used for things that cause anxiety, stress, or agitation.

In Spanish, the subject can be an action or clause without needing a separate word like English it.

English often uses it as a placeholder:

• It makes me nervous to arrive late...

Spanish does not need that placeholder here:

• Me pone nervioso llegar...

The action itself is the subject.

Yes, both can be possible, but they are not always identical in tone.

• llegar con retraso = to arrive with a delay / to arrive late
• llegar tarde = to arrive late

In this sentence, con retraso sounds slightly more formal or neutral, which fits well with a una entrevista.
Llegar tarde a una entrevista is also very natural and probably even more common in everyday speech.

Here a means to:

• llegar a una entrevista = to arrive at an interview

It is the preposition used with llegar to indicate the destination or event you are arriving at.

Spanish often uses an article where English might be more flexible.

• a una entrevista = to an interview

Using una sounds natural because it refers to a particular type of situation: arriving late to an interview.
Without the article, a entrevista, would be ungrammatical here.

Yes. Spanish allows some flexibility, although the original order is very natural.

These are possible:

• Me pone nervioso llegar con retraso a una entrevista.
• Llegar con retraso a una entrevista me pone nervioso.

The second version emphasizes the action first. Both are correct.

Usually it sounds general: the speaker is saying that being late for a job interview is something that makes them nervous.

Because it uses the infinitive llegar and una entrevista, it expresses a general situation rather than one specific event.
If the speaker meant a specific interview, context would usually make that clear.

Not with the same meaning.

• Me pone nervioso llegar con retraso... = The idea/situation of arriving late makes me nervous
• Estoy nervioso... = I am nervous

So me pone nervioso focuses on the cause of the feeling.
Estoy nervioso describes your current state.

A more natural alternative with estar would be something like:

• Estoy nervioso porque voy a llegar con retraso a una entrevista.

That means you are nervous because you are going to be late, not that lateness in general makes you nervous.

Yes, very much. This pattern is extremely useful:

[indirect object pronoun] + poner + adjective + infinitive/clause

Examples:

• Me pone triste escuchar esa canción.
  That song makes me sad / լսening to that song makes me sad.

• Nos pone contentos veros aquí.
  Seeing you here makes us happy.

• Le pone de mal humor esperar tanto.
  Waiting so long puts him/her in a bad mood.

It is a very natural way to talk about what causes feelings.