W tym warsztacie sprawdzają hamulce, silnik i światła.

Because after w meaning in/at for location, Polish normally uses the locative case.

• dictionary form: ten warsztat = this workshop / this garage
• locative after w: w tym warsztacie = in/at this workshop

So:

• tym is the locative form of ten
• warsztacie is the locative form of warsztat

In this sentence, warsztat most naturally means an auto repair shop / garage. A very natural English translation would be At this garage or In this repair shop.

So W tym warsztacie... is more about the place where cars are serviced, not a school workshop or craft studio.

The verb form sprawdzają already tells you it is 3rd person plural: they check.

Polish often leaves out subject pronouns when they are obvious from the verb ending. Here it means something like:

• they check
• the staff check
• people check

In this kind of sentence, it often has a general meaning: this is what they do there.

Sprawdzają is the present tense, 3rd person plural, of the imperfective verb sprawdzać = to check.

It is used because the sentence describes a regular service or general activity:

• W tym warsztacie sprawdzają... = In this workshop, they check...

If you used the perfective verb sprawdzić, the form sprawdzą would usually mean they will check, not they check.

It can mean either, depending on context. Polish present tense often covers both:

• they are checking
• they check / they usually check

In this sentence, with W tym warsztacie..., the most natural reading is a general service description: this is what they check there.

Yes. They are the direct objects of sprawdzają, so they are in the accusative case.

But for these nouns, the accusative looks the same as the nominative:

• silnik is masculine inanimate singular, so accusative = nominative
• hamulce is an inanimate plural, so accusative = nominative
• światła is a neuter plural, so accusative = nominative

So they do not visibly change here, even though they are objects.

Because that is simply how these things are normally referred to.

• hamulce = brakes → naturally plural
• silnik = engine → usually singular
• światła = lights → naturally plural

So the sentence lists the things a garage checks: brakes, engine and lights.

It is plural.

• singular: światło = light
• plural: światła = lights

In a car-related context, światła usually means the vehicle’s lights, such as headlights, brake lights, and so on.

Yes. Polish word order is fairly flexible.

The version here, W tym warsztacie sprawdzają hamulce, silnik i światła, is neutral and natural.

You could also say:

• Hamulce, silnik i światła sprawdzają w tym warsztacie.

That is still grammatical, but it shifts the emphasis more onto what they check. The original sentence sounds more natural as a general description.

Because Polish has no articles. There is no direct equivalent of a / an / the used in ordinary sentences the way English uses them.

So Polish simply says:

• w tym warsztacie = in this workshop
• sprawdzają hamulce, silnik i światła = they check brakes, the engine and the lights / they check brakes, engine and lights

English needs articles more often; Polish does not.

Because i means and, and in a simple list Polish normally does not put a comma before it.

So:

• hamulce, silnik i światła = brakes, engine and lights

That is standard Polish punctuation.