Zjistím, jestli ojeté auto používá benzin, nebo naftu.

Because zjistit is a perfective verb. In Czech, perfective verbs use present-tense forms to express a future completed action.

So:

• zjistím = I will find out
• not I am finding out

If you wanted an ongoing present meaning, you would use the imperfective verb zjišťovat:

• Zjišťuji / zjišťuju = I’m finding out / I’m checking

Czech usually omits subject pronouns when they are clear from the verb ending.

Here, -ím in zjistím already tells you the subject is I. So já is not necessary.

• Zjistím = I will find out
• Já zjistím = I will find out with extra emphasis, contrast, or insistence

For example, Já zjistím could sound like I’ll find out (not someone else).

Here jestli means whether / if in an indirect question.

So:

• Zjistím, jestli... = I’ll find out whether...

This is a very common pattern after verbs like:

• vědět = to know
• ptát se = to ask
• zjistit = to find out

In this sentence, jestli ... benzin, nebo naftu corresponds to whether ... petrol/gasoline or diesel.

The comma after Zjistím is there because jestli introduces a subordinate clause. That comma is standard and expected:

• Zjistím, jestli...

The comma before nebo is less essential. Many speakers would simply write:

• Zjistím, jestli ojeté auto používá benzin nebo naftu.

Since benzin and naftu are just two coordinated alternatives, the second comma is often omitted.

Ojeté auto means a used car.

The adjective ojetý literally suggests something like used/driven/worn from use, and in car-related contexts it commonly means used or second-hand.

The form ojeté is used because auto is:

• neuter
• singular
• here the subject of the clause

So the adjective has to agree with auto:

• ojetý = masculine
• ojetá = feminine
• ojeté = neuter

Používá is the 3rd person singular form of používat (to use).

It matches the subject ojeté auto:

• auto používá = the car uses

Even though auto is neuter, in the present tense the verb form for he/she/it is the same:

• on používá
• ona používá
• ono používá

So auto používá is grammatically exactly what you would expect.

Because both words are direct objects after používá, so they are in the accusative case. But different nouns change differently.

• benzin is a masculine inanimate noun, and in the singular its accusative is the same as its nominative.
• nafta is a feminine noun, and its accusative singular changes to naftu.

So:

• benzin → benzin
• nafta → naftu

This is a very common thing in Czech declension.

It is understandable, but it sounds a bit more literal than what many native speakers would naturally say.

More idiomatic options are often:

• Zjistím, jestli to ojeté auto jezdí na benzin, nebo naftu.
• Zjistím, jestli je to auto na benzin, nebo naftu.

Czech often uses jezdit na + fuel for vehicles:

• auto jezdí na benzin
• auto jezdí na naftu

So your original sentence is grammatical, but not the most everyday phrasing.

Yes. Zda also means whether.

So you can say:

• Zjistím, zda ojeté auto používá benzin, nebo naftu.

The difference is mostly one of style:

• jestli = more common in everyday speech
• zda = a bit more formal or written

Both are correct here.

Because Czech has no articles like English a/an/the.

So ojeté auto can mean:

• a used car
• the used car

The exact meaning depends on context.

If Czech wants to be more specific, it can use other words, for example:

• to ojeté auto = that/this used car
• nějaké ojeté auto = some used car

But very often Czech simply leaves articles out, because the language does not have them.