Si la roue arrière fait encore du bruit demain, nous prendrons le train au lieu de la voiture.

In French, a real future condition is usually built like this:

• Si + present tense, then
• future tense in the main clause

So:

• Si la roue arrière fait encore du bruit demain = if the rear wheel is still making noise tomorrow
• nous prendrons le train = we will take the train

This is the normal pattern for likely or possible future situations.

A very common mistake for English speakers is to say si ... fera, but that is not standard here.

Examples:

• Si tu viens demain, je serai là.
• Si il pleut, nous resterons à la maison.

Faire du bruit is a very common French expression meaning to make noise or to be noisy.

So:

• La roue fait du bruit = the wheel is making noise

French often uses faire in places where English uses a different verb. You should learn faire du bruit as a set expression.

Related examples:

• Les enfants font du bruit. = The children are making noise.
• Cette machine fait un bruit bizarre. = This machine is making a strange noise.

Notice that French can say either:

• faire du bruit = make noise in general
• faire un bruit = make a particular noise

Because in French, bruit here is a noun, and nouns usually need some kind of article or determiner.

Du is the partitive article here, often used when talking about an unspecified amount or general idea of something.

So:

• faire du bruit = to make noise / to be noisy

You usually would not say just faire bruit.

Compare:

• boire de l’eau = to drink water
• faire du bruit = to make noise

Even though English often leaves out the article, French usually does not.

Here encore means still.

So:

• fait encore du bruit demain = is still making noise tomorrow

Depending on context, encore can also mean again, which can confuse learners.

Examples:

• Il pleut encore. = It’s still raining.
• Dis-le encore. = Say it again.

In your sentence, still is clearly the right meaning because the idea is that the wheel is already making noise now, and maybe it will continue tomorrow.

In French, many adjectives come after the noun, and arrière is one of them in this kind of expression.

So:

• la roue arrière = the rear wheel

This is the normal order.

French often puts descriptive adjectives after the noun:

• une voiture rouge = a red car
• une porte arrière = a rear door

Also, arrière in this use is invariable, so it does not change form:

• la roue arrière
• les roues arrière

Yes. In French, prendre is very commonly used to mean take when talking about transport.

So:

• prendre le train = take the train
• prendre le bus = take the bus
• prendre l’avion = take the plane

This works much like English.

In your sentence:

• nous prendrons is the future tense of prendre
• infinitive: prendre
• future stem: prendr-
• ending for nous: -ons
• so: nous prendrons

Prendrons comes from prendre, which has an irregular future stem:

• infinitive: prendre
• future stem: prendr-
• full form: nous prendrons

The d is part of that stem. Many common verbs have irregular future stems in French.

Other examples:

• avoir → j’aurai
• être → je serai
• venir → je viendrai
• prendre → je prendrai

So you just need to memorize prendr- for the future and conditional.

Au lieu de means instead of or in place of.

In your sentence:

• au lieu de la voiture = instead of the car

It is a fixed expression.

You can use it before:

• a noun: au lieu du bus
• a pronoun: au lieu de lui
• an infinitive: au lieu de partir = instead of leaving

Examples:

• Nous marcherons au lieu de prendre la voiture.
• Elle a choisi le thé au lieu du café.

Because au lieu de must be followed by de, and then the noun keeps its article as needed.

So:

• de + la voiture = de la voiture

With other articles, contractions happen:

• de + le = du
• de + les = des

Examples:

• au lieu du train = instead of the train
• au lieu des bus = instead of the buses
• au lieu de la voiture = instead of the car

Not in the same structure.

En voiture usually means by car or in the car, but your sentence is contrasting two options:

• prendre le train
• la voiture

So au lieu de la voiture means instead of the car.

If you rewrote the sentence, you could say something like:

• ... nous irons en train au lieu d’y aller en voiture.

That would be more like:

• we will go by train instead of going by car

But the original sentence is perfectly natural as it is.

French word order is often flexible with time expressions like demain, but this placement is very natural.

• Si la roue arrière fait encore du bruit demain
  means
• If the rear wheel is still making noise tomorrow

Putting demain near the end lets the sentence build naturally:

1. subject: la roue arrière
2. verb phrase: fait encore du bruit
3. time: demain

You could also hear:

• Si demain la roue arrière fait encore du bruit...

That is possible, but it gives demain more emphasis.

Yes, this is completely natural everyday French.

It sounds like normal spoken or written French. Nothing in it is overly formal.

The sentence contains several very common everyday patterns:

• si + present
• faire du bruit
• prendre le train
• au lieu de

A speaker might also say a slightly simpler version in casual conversation, for example:

• Si la roue arrière fait encore du bruit demain, on prendra le train plutôt que la voiture.

Here on replaces nous, which is very common in speech. But your original sentence is still entirely normal.