Jeżeli oświetlenie działa, diagnosta dopuści pojazd do ruchu.

Jeżeli means if.

In this sentence, it introduces the condition:

• Jeżeli oświetlenie działa = If the lighting works

Yes, jeżeli and jeśli are usually interchangeable in everyday Polish.
Jeżeli can sound a little more formal or slightly more emphatic, but in most contexts both are fine.

So you could also say:

• Jeśli oświetlenie działa, diagnosta dopuści pojazd do ruchu.

Because Polish normally uses a comma to separate a subordinate clause from the main clause.

Here the first part is the condition clause:

• Jeżeli oświetlenie działa = If the lighting works

And the second part is the main clause:

• diagnosta dopuści pojazd do ruchu = the inspector will approve the vehicle for road use

So the comma is standard Polish punctuation here.

Because the condition is stated as a general present fact:

• oświetlenie działa = the lighting works / is functioning

That is normal in both Polish and English in if clauses. Compare:

• If the lighting works, ...
• not usually If the lighting will work, ...

So Polish is following the same logic here.

This is a very common Polish grammar point.

Dopuścić is a perfective verb. In Polish, the present-tense forms of perfective verbs usually refer to the future, not the present.

So:

• dopuści literally looks like a present form
• but its meaning is will approve / will allow

This is different from an imperfective verb, whose present form usually has true present meaning.

So in this sentence:

• diagnosta dopuści pojazd do ruchu = the inspector will approve the vehicle for road use

Diagnosta is a noun meaning a diagnostician / inspector / examiner, depending on context.

In this sentence it specifically means a vehicle inspection technician or roadworthiness inspector — the person who checks whether a vehicle meets technical requirements.

Although the word ends in -a, it is a masculine personal noun when referring to a man, like several Polish profession words such as:

• artysta
• kierowca
• mężczyzna

So here diagnosta is the subject of the sentence.

Because pojazd is the direct object of dopuści.

The verb dopuścić takes an object in the accusative case:

• dopuścić kogo? co?
• pojazd

Since pojazd is a masculine inanimate noun, its accusative singular is the same as its nominative singular:

• nominative: pojazd
• accusative: pojazd

So even though it is an object, the form does not change.

Ruchu is in the genitive case.

That is because of the preposition do, which normally requires the genitive:

• do + genitive

So:

• ruch = nominative
• do ruchu = genitive

The phrase dopuścić pojazd do ruchu is a standard expression meaning:

• to approve a vehicle for use on public roads
• literally something like to admit the vehicle to traffic

It is a fixed and very common official phrase in transport/inspection language.

Oświetlenie literally means lighting.

In this sentence, it refers to the vehicle’s lighting system — for example:

• headlights
• brake lights
• indicators
• other required lights

It is a neuter noun:

• nominative singular: oświetlenie

So:

• oświetlenie działa = the lighting works / the lights are functioning

Even though English often uses plural lights, Polish can use the singular collective noun oświetlenie.

Because działać means to work / to function / to operate.

That is the most natural verb when talking about whether a system is functioning properly.

So:

• oświetlenie działa = the lighting works / is functioning

By contrast:

• jest would just mean is, which would not express proper functioning
• świeci means shines / gives light, which is more literal and narrower

For technical inspections, działa is exactly the kind of word you would expect.

Yes. Polish word order is fairly flexible, although the neutral order here is very natural.

Original:

• Jeżeli oświetlenie działa, diagnosta dopuści pojazd do ruchu.

You could also reverse the clauses:

• Diagnosta dopuści pojazd do ruchu, jeżeli oświetlenie działa.

Both mean the same thing:
If the lighting works, the inspector will approve the vehicle for road use.

The original version puts the condition first, which is very common.

It is mostly official, technical, or administrative language.

You often see it in contexts like:

• vehicle inspections
• safety regulations
• roadworthiness documents
• legal/administrative decisions

A more everyday way to express the general idea might be something like:

• pozwolić używać pojazdu na drodze
• zatwierdzić pojazd do jazdy

But in the context of inspections, dopuścić pojazd do ruchu is the standard and correct phrase.

Not in this sentence if you want to keep the clear if meaning.

Polish usually needs an explicit word like:

• jeżeli
• jeśli
• sometimes gdy or kiedy in different contexts

Without jeżeli, the sentence would no longer clearly mean if the lighting works, ...

So here it should stay.

Then Polish would probably use an imperfective verb instead of perfective dopuści.

For example:

• Jeżeli oświetlenie działa, diagnosta dopuszcza pojazd do ruchu.

That would mean something more like:

• If the lighting works, the inspector approves/admits the vehicle for road use
• in the sense of a general rule or repeated procedure

But your original sentence with dopuści sounds like a specific future outcome:

• the inspector will approve the vehicle

So the verb choice helps show whether we mean a general rule or a specific future act.