Learn Hardcore French: Chaque pompier porte un casque de sécurité et une grande veste. - Each firefighter wears a safety helmet and a big jacket.

chaque pompier – focuses on individuals, one by one:
“Each firefighter (individually) wears a safety helmet and a big jacket.”
tous les pompiers – focuses on the group as a whole:
“All the firefighters wear a safety helmet and a big jacket.”

Grammatically:

chaque pompier porte… (singular subject + singular verb)
tous les pompiers portent… (plural subject + plural verb)

Why is the verb porte and not portes or something else?

The verb is porter (“to wear / to carry”). In the present tense:

je porte
tu portes
il / elle / on porte
nous portons
vous portez
ils / elles portent

The subject here is chaque pompier, which works like il (he) or elle (she) grammatically: 3rd person singular.
So we use porte:

chaque pompier porte … (not portes, not portent).

Why do we use un casque and une veste (indefinite articles) and not le casque or la veste?

Un / une are indefinite articles (“a / an”). They’re used because we’re talking about one such item per firefighter, not a specific, previously mentioned item:

un casque de sécurité – a safety helmet (one helmet of that type)
une grande veste – a big jacket (one jacket of that type)

If you said:

le casque de sécurité et la grande veste

it would sound like you’re referring to the specific helmet and the specific jacket already known from context, which is not the idea here.

What exactly does casque de sécurité mean, and why is it de without an article?

Un casque de sécurité literally = “a helmet of safety,” but idiomatically it means “a safety helmet”.

The structure is:

casque (helmet) + de
- sécurité (safety)

Here, de + noun is used to show type or purpose, similar to English “safety helmet,” “tennis racket,” “coffee cup,” etc.

We don’t add an article in front of sécurité:

✔ un casque de sécurité
✘ un casque de la sécurité (sounds like “the safety’s helmet,” which is wrong here)

So de sécurité is functioning like an adjectival complement, describing what kind of helmet it is.

Why is it une grande veste and not un grand veste?

Because veste is a feminine noun in French:

la veste – the jacket

Adjectives and articles must agree in gender and number with the noun:

une veste (feminine singular)
une grande veste (feminine singular article + feminine singular adjective + noun)

So:

une grande veste ✔
un grand veste ✘ (wrong gender for both article and adjective)

Why does grande come before the noun, but in English “big” usually comes before “jacket” too—so is this always the case?

In French, adjectives can come before or after the noun, unlike English where they almost always come before.

However, a few categories of adjectives very often come before the noun. A common teaching trick is BANGS (Beauty, Age, Number, Goodness, Size):

Beauty: beau, joli
Age: vieux, jeune, nouveau
Number: un, deux, trois, plusieurs, etc.
Goodness: bon, mauvais, meilleur
Size: grand, petit, gros, etc.

Grande (big/tall) is a size adjective, so it normally comes before:

une grande veste

Many other adjectives, especially ones of color, shape, nationality, material, come after the noun:

une veste rouge – a red jacket
une veste française – a French jacket

What is the difference between grand and grande?

They are the same adjective, but they change form to agree with the noun:

grand – masculine singular
grande – feminine singular
grands – masculine plural
grandes – feminine plural

So:

un grand pompier – a tall/big (male) firefighter
une grande veste – a big jacket
de grands pompiers – great firefighters
de grandes vestes – big jackets

Could we say une veste grande instead of une grande veste?

In normal, neutral French, une grande veste is the natural order.
Putting grande after veste is unusual here and would sound either:

poetic / stylistic, or
very marked, with a different nuance (e.g. emphasizing size in a special way)

For everyday speech and writing, stick with:

une grande veste ✔

Is pompier only masculine? How would you talk about female firefighters?

Traditionally, pompier is used for a male firefighter, and in many contexts it is now used in a gender-neutral way (“firefighter” in general).

There is also a feminine form:

une pompière – a female firefighter

Plurals:

les pompiers – (male or mixed-gender group)
les pompières – group of only female firefighters

In your sentence, chaque pompier can be understood generically (“each firefighter”), not just male.

Does porter here mean “to wear” or “to carry”? How do I say “put on”?

Porter can mean both “to wear” and “to carry”, depending on context.

With clothes, shoes, accessories: porter = to wear.
Chaque pompier porte un casque de sécurité – Each firefighter wears a safety helmet.
With objects in your hands or on your back: porter = to carry.
Il porte un sac lourd. – He is carrying a heavy bag.

To say “to put on” (clothes), you use mettre:

Chaque pompier met un casque de sécurité avant l’intervention.
Each firefighter puts on a safety helmet before the operation.

Why is it et une grande veste and not just et grande veste?

In French, when you list two different nouns, each normally keeps its article:

un casque de sécurité et une grande veste – a safety helmet and a big jacket

You cannot drop the article before the second noun in this structure:

✘ un casque de sécurité et grande veste

Compare:

un chat et un chien
une table et une chaise

How is this sentence pronounced, especially chaque and pompier?

Approximate pronunciation (in simple English-style syllables):

Chaque – “shak” (short a as in “cat,” but a bit more open; final -e is silent)
pompier – “pohn-pee-eh” [pɔ̃-pje], where:
- pom- uses a nasal vowel: the m is not fully pronounced, so it sounds like “pohn” with the sound going through the nose
- -pier sounds like “pyeh” (one syllable: pje)

Whole sentence, very roughly:

Chaque pompier porte un casque de sécurité et une grande veste.
“Shak pohn-pyeh port un kask duh say-kü-ri-tay ay ühn grand vest.”

(That’s only an approximation; IPA would be:
[ʃak pɔ̃pje pɔʁt œ̃ kask də sekyʁite e yn gʁɑ̃d vɛst].)

If I want to make the sentence clearly plural, how would I change it?

You can use tous les pompiers instead of chaque pompier. Then you must also change the verb and possibly the rest if needed:

Tous les pompiers portent un casque de sécurité et une grande veste.
All the firefighters wear a safety helmet and a big jacket.

Changes:

chaque pompier porte → tous les pompiers portent (subject and verb become plural)
The objects (un casque, une grande veste) stay singular because each firefighter still has one of each.