Disculpe, he llegado tarde.

Disculpe means something like Excuse me or Please forgive me.

In this sentence, it is being used as a polite way to get the other person’s attention and apologize before giving the reason: I’ve arrived late.

It comes from the verb disculpar = to excuse / to forgive.

Disculpe is the formal form, used with usted.
Disculpa is the informal form, used with tú.

So:

• Disculpe = polite / formal / respectful
• Disculpa = informal / familiar

In Spain, you would use Disculpe with someone you do not know well, a teacher, an older person, or in a professional situation.

He llegado is the present perfect: I have arrived. In Spain, this tense is very commonly used for actions connected to the present moment.

Here, the speaker is apologizing for something that has just happened or is still relevant now: they are late right now.

Compare:

• He llegado tarde = I’ve arrived late / I’m late; I arrived late
• Llegué tarde = I arrived late

In many parts of Spain, he llegado tarde sounds very natural in this kind of immediate situation.

Yes, literally it does. But in natural English, you would often translate it simply as:

• I’m late
• I arrived late
• Sorry I’m late

So even though the Spanish structure is I have arrived late, the best English translation depends on the situation.

Spanish often leaves out subject pronouns because the verb form already shows who is doing the action.

• he llegado clearly means I have arrived

So yo is not necessary. You could say Yo he llegado tarde, but it would usually sound unnecessary unless you want emphasis, contrast, or clarification.

Here, tarde is an adverb, meaning late.

It describes how the person arrived:

• llegar tarde = to arrive late

Because it is an adverb here, it does not change for gender or number.

Compare:

• He llegado tarde = I arrived late
• La hora tardía = the late hour

In the sentence you gave, tarde is the fixed form you want.

Yes. Llegar tarde is the normal way to say to arrive late.

Examples:

• Siempre llegas tarde. = You always arrive late.
• Llegué tarde a clase. = I arrived late to class.

It is a very common and useful expression.

Yes, depending on the tone.

Common options are:

• Disculpe = polite, formal, slightly more careful
• Perdón = Sorry / Excuse me, very common
• Lo siento = I’m sorry, often sounds a bit more emotional or sincere

For example:

• Disculpe, he llegado tarde.
• Perdón, he llegado tarde.
• Lo siento, he llegado tarde.

All are possible, but Disculpe is especially appropriate if you want to sound respectful.

You would normally change Disculpe to Disculpa if speaking to one person informally.

So:

• Disculpa, he llegado tarde.

If you are talking to friends or people your age in a casual setting, this is more natural.

The h in Spanish is silent, so he is pronounced roughly like eh.

So:

• he llegado sounds like eh yeh-GAH-do (very roughly)

Also, ll in most of Spain is usually pronounced like y in many modern accents, though exact pronunciation can vary by region.

Yes, it is completely natural and can stand on its own.

Disculpe, he llegado tarde. is a clear, polite apology.

If you want to sound a bit fuller or more apologetic, you could add something like:

• Disculpe, he llegado tarde. Ha habido mucho tráfico.
  Excuse me, I’ve arrived late. There was a lot of traffic.

But the original sentence is already correct and natural.

No. Estoy tarde is not the normal way to say I’m late in Spanish.

Spanish usually expresses this idea with llegar tarde:

• He llegado tarde
• Llego tarde
• Llegué tarde

You may also hear Voy tarde = I’m running late, especially when the person has not arrived yet.

They are related, but not the same.

• he llegado tarde = I have arrived late / I arrived late
• llego tarde = I am arriving late / I arrive late / I’m late

If you are already there and apologizing for being late, he llegado tarde works very well.

If you are on the way or speaking more generally about the situation, llego tarde may fit better.

For example:

• On the phone before arriving: Llego tarde.
• After arriving: Disculpe, he llegado tarde.