Quatre personnes arrivent.

Because quatre personnes is the subject, and it is plural.

In French, the verb agrees with the subject:

• Une personne arrive = One person arrives
• Quatre personnes arrivent = Four people arrive / are arriving

So the -ent ending shows that the subject is they/plural.

Usually, no.

In modern spoken French:

• arrive = pronounced a-reev
• arrivent = also pronounced a-reev

The -ent ending is important in writing because it shows plural agreement, but it is normally silent.

Because French normally does not use an article before a noun when it is directly preceded by a number.

So you say:

• quatre personnes
• trois livres
• deux voitures

Not:

• les quatre personnes unless you mean the four people specifically

In your sentence, quatre personnes just means four people in a general way.

Because it is plural.

The singular is:

• une personne = one person

The plural is:

• deux personnes
• quatre personnes

The final -s marks the plural in writing, but it is usually not pronounced.

Because quatre does not change for gender.

Most French numbers stay the same whether the noun is masculine or feminine:

• quatre hommes
• quatre personnes
• quatre maisons

Only some words, especially un / une, change for gender:

• un homme
• une personne

So quatre stays quatre.

Yes, but not here.

French personne has two uses:

1. As a noun, meaning person

   • une personne
   • quatre personnes

2. As part of a negative expression, meaning nobody / no one

   • Je ne vois personne = I see nobody

In Quatre personnes arrivent, it is clearly the noun meaning people/persons, because it comes after a number.

A simple English-style guide is:

katr pehr-son a-reev

A more French-based breakdown is:

• quatre = /katʁ/
• personnes = /pɛʁ.sɔn/
• arrivent = /a.ʁiv/

A few useful pronunciation notes:

• the -s in personnes is silent
• the -ent in arrivent is silent
• the French r is not like the English r; it is made farther back in the mouth/throat

It can mean either, depending on context.

The French present tense often covers both:

• the English simple present: Four people arrive
• the English present progressive: Four people are arriving

In many real situations, if you are describing something happening now, are arriving is the more natural English translation.

Because after an exact number, personnes is the normal word.

French usually says:

• deux personnes
• quatre personnes
• dix personnes

Gens means people, but it is more general and is not normally used directly after a number. So quatre personnes sounds natural, while quatre gens does not.

Yes, that is possible, but it is a different structure.

• Quatre personnes arrivent is a direct sentence with quatre personnes as the subject.
• Il y a quatre personnes qui arrivent is closer to There are four people arriving.

Both are grammatical, but Quatre personnes arrivent is shorter and more direct.