Hoy hay más de mil personas en el estadio.

Because hay means there is / there are in an impersonal, existential sense: it introduces the existence of something.

• Hay más de mil personas en el estadio = There are more than a thousand people in the stadium
• Están would be used when the people are already known or identified, and you are saying where they are:
  • Las personas están en el estadio = The people are in the stadium

A very common rule is:

• hay = there is / there are
• está / están = is / are located

Also, hay does not change for singular or plural:

• Hay una persona
• Hay mil personas

Hoy means today.

It is placed at the beginning to set the time context right away:

• Hoy hay más de mil personas en el estadio = Today, there are more than a thousand people in the stadium

Spanish often puts time expressions at the beginning, but other positions are also possible:

• Hay más de mil personas en el estadio hoy

That said, starting with hoy sounds very natural because it highlights today as the important contrast.

In Spanish, when you say more than + number, you normally use más de.

So:

• más de mil = more than a thousand
• más de veinte = more than twenty
• más de dos horas = more than two hours

Without de, it would be incorrect here.

Because mil normally does not take un when it means one thousand.

So you say:

• mil personas = one thousand people
• más de mil personas = more than a thousand people

Compare that with:

• un millón = one million
• un billón in Spanish has a different meaning from English, but it does take un

So:

• mil stands alone
• millón needs an article or another determiner

Both can refer to people, but they are used differently.

• personas = countable individuals
• gente = people as a collective group

In this sentence, since there is a specific number, personas is the natural choice:

• más de mil personas

You generally do not say:

• más de mil gente ✘

You could say:

• Hay mucha gente en el estadio = There are lots of people in the stadium

So:

• use personas with numbers
• use gente for a general mass of people

Because grammatical gender and real-life gender are not always the same thing.

The noun persona is grammatically feminine, so adjectives and articles agree with it in the feminine:

• una persona
• muchas personas

But it can refer to anyone:

• a man can be una persona
• a woman can be una persona

This is normal in Spanish. The grammar follows the noun, not necessarily the biological sex of the person being referred to.

Because en shows location: the people are in the stadium.

• en el estadio = in the stadium / at the stadium

By contrast, al estadio usually shows movement to the stadium:

• Voy al estadio = I’m going to the stadium

So in your sentence, the people are already there, which is why en is used.

Yes, estadio is a masculine noun, so it takes el:

• el estadio

Many nouns ending in -o are masculine, and estadio follows that common pattern.

So:

• el estadio grande
• en el estadio

Yes. Hay is invariable in this use.

You use hay for both singular and plural:

• Hay una persona
• Hay dos personas
• Hay más de mil personas

This is one of the most important things to remember about hay.

Yes, Spanish word order is fairly flexible, though some orders sound more natural depending on what you want to emphasize.

Your sentence:

• Hoy hay más de mil personas en el estadio

Other possible versions:

• En el estadio hay más de mil personas hoy
• Hay más de mil personas en el estadio hoy

These are grammatically possible, but the original sounds very natural because it introduces the time first and then states the situation.

Normally, no. That sounds unnatural in standard Spanish for this meaning.

If you want to express there are more than a thousand people, use:

• Hoy hay más de mil personas en el estadio

Using están would require the people to be treated as specific, known people:

• Hoy las personas están en el estadio

So for existence or presence in general, hay is the correct choice.

They are similar, but not identical.

• más de mil personas = more than a thousand people
  This is neutral and precise enough for standard speech.
• mil y pico personas = a thousand and a bit people / a little over a thousand people
  This is more informal and suggests only slightly more than a thousand.

So your sentence sounds more standard and neutral.

In standard Spanish pronunciation:

• h is silent
• hay sounds roughly like eye in English

So:

• hay ≈ eye

This can be confusing because it is written with h, but you do not pronounce the h at all.