Bez ohledu na palivo prověříme motor a brzdový kotouč.

It means regardless of or irrespective of.

Literally:

• bez = without
• ohled = regard / consideration
• na = to / for / with respect to, depending on context

So bez ohledu na palivo is an idiomatic way to say regardless of the fuel or no matter what fuel it is.

Good question. On its own, bez does take the genitive, for example:

• bez vody = without water

But bez ohledu na is a fixed expression. In this expression:

• bez goes with ohledu (genitive of ohled)
• na then introduces the thing being disregarded

So the structure is:

• bez ohledu na + accusative

That is why you get:

• bez ohledu na palivo

not just bez ohledu paliva.

It is in the accusative singular, because na in the expression bez ohledu na requires the accusative.

With palivo, the nominative and accusative singular look the same, because it is a neuter noun:

• nominative: palivo
• accusative: palivo

So even though the form does not change, the case is still accusative.

Palivo means fuel in a general sense. It can refer to:

• petrol/gasoline
• diesel
• gas
• other fuels

In this sentence, it most naturally means the type of fuel or whatever fuel is involved.

So bez ohledu na palivo suggests something like:

• regardless of the fuel type
• no matter what fuel the vehicle uses

Prověříme means we will check, we will inspect, we will verify, or we will examine thoroughly, depending on context.

The base verb is prověřit, which often suggests a fairly thorough check or verification, not just a quick glance.

In a technical context like this, translations such as these are natural:

• we will inspect
• we will check
• we will test

That is because prověřit is a perfective verb.

In Czech, perfective verbs do not normally have a true present meaning. Their present-tense forms usually refer to the future.

So:

• prověříme literally looks like a present form
• but it means we will check / we will inspect

This is very common in Czech.

Compare:

• ověřujeme = we are verifying / we verify (imperfective)
• ověříme = we will verify (perfective)

Because Czech usually does not need subject pronouns when the verb ending already shows who the subject is.

In prověříme, the ending -me tells you the subject is we.

So:

• prověříme = we will check

You could say my prověříme, but that would usually add emphasis, something like:

• we will check it

In a neutral sentence, leaving out my is normal.

They are direct objects, so they are in the accusative. But both are masculine inanimate nouns, and for many masculine inanimate nouns, the accusative singular is the same as the nominative singular.

So you get:

• nominative: motor
• accusative: motor

and

• nominative: kotouč
• accusative: kotouč

The adjective also matches the noun:

• nominative masculine inanimate singular: brzdový
• accusative masculine inanimate singular: brzdový

So the forms do not visibly change here, even though the case is accusative.

It is one noun phrase:

• brzdový = brake / braking
• kotouč = disc

Together, brzdový kotouč means brake disc or brake rotor.

So the sentence is talking about checking two things:

• motor
• brzdový kotouč

Czech often uses adjectives where English may use a noun as a modifier.

English:

• brake disc

Czech:

• brzdový kotouč
• literally: braking/brake-related disc

This is very common. Another example:

• motorový olej = engine oil
• literally: motor-related oil

So brzdový kotouč is the normal Czech way to say brake disc.

Yes, it could be rearranged. Czech word order is flexible, and the version you have is natural because it starts with the condition/frame:

• Bez ohledu na palivo = setting the context first
• prověříme motor a brzdový kotouč = then the main action

This ordering sounds natural and slightly formal or technical.

You could also say:

• Prověříme motor a brzdový kotouč bez ohledu na palivo.

That still means basically the same thing, but the emphasis is a little different. The original version highlights regardless of the fuel from the start.

No. Czech has no articles like a/an/the.

So:

• motor can mean an engine or the engine
• brzdový kotouč can mean a brake disc or the brake disc

The exact meaning depends on context. In this sentence, English would often use the because we are probably talking about a specific vehicle or system:

• we will inspect the engine and the brake disc

But Czech expresses that without articles.

It sounds somewhat formal and technical, especially because of:

• bez ohledu na = a fairly formal connector
• prověříme = a more technical/formal verb than a very casual zkontrolujeme
• brzdový kotouč = technical vocabulary

It would fit well in:

• service instructions
• technical documentation
• a maintenance checklist
• a professional statement

In everyday speech, someone might choose simpler wording, but this sentence is completely natural.