Cuanto más rápido va la bicicleta, más fuerte frenamos.

It is the Spanish equivalent of the English correlative comparative the more..., the more....

So:

• Cuanto más rápido va la bicicleta, más fuerte frenamos.
• The faster the bicycle goes, the harder we brake.

This pattern links two changes together:

• one thing increases or changes
• and another thing increases or changes as a result

A very common formula is:

• Cuanto más + clause, más + clause

You can also see similar patterns with menos:

• Cuanto más estudias, menos dudas tienes.
• The more you study, the fewer doubts you have.

Because here cuanto is not a question word or exclamation word.

In Spanish, the accented forms like cuánto, qué, cómo, cuándo are usually used in:

• direct questions
• indirect questions
• exclamations

Examples:

• ¿Cuánto cuesta?
• No sé cuánto cuesta.

But in your sentence, cuanto is functioning as part of a comparative connector: cuanto más..., más.... In that use, it normally has no accent.

No. They are different words.

• cuando = when
• cuanto = how much / as much as / the more... depending on context

In this sentence, cuanto is part of the structure cuanto más..., más..., so it has nothing to do with time.

Compare:

• Cuando va rápido, frenamos. = When it goes fast, we brake.
• Cuanto más rápido va, más fuerte frenamos. = The faster it goes, the harder we brake.

That is a big meaning difference.

Spanish word order is more flexible than English word order.

In this sentence, más rápido is placed before the verb for emphasis and because it fits naturally in the comparative structure:

• Cuanto más rápido va la bicicleta...

This sounds natural.

You could also say:

• Cuanto más rápido va la bici...

But Cuanto más rápido la bicicleta va... sounds much less natural.

So the main point is: after fronting más rápido, Spanish often places the verb before the subject.

Because Spanish very often uses adjectives adverbially in everyday speech, especially with verbs of movement.

So:

• ir rápido = to go fast
• hablar alto = to speak loudly
• trabajar duro = to work hard

Even though rápidamente is grammatically possible, va rápido is much more natural in normal speech.

So:

• la bicicleta va rápido = very natural
• la bicicleta va rápidamente = correct, but more formal or stiff

For the same reason: Spanish often prefers a simple adjective used adverbially in everyday language.

So:

• frenar fuerte = to brake hard
• frenar más fuerte = to brake harder

This is very common and natural.

You may also hear:

• frenar con más fuerza

That means almost the same thing and can sound a little more explicit.

Fuertemente is not wrong, but it is less common in ordinary speech here.

Because Spanish often omits subject pronouns when the verb ending already makes the subject clear.

• freno = I brake
• frenas = you brake
• frenamos = we brake

So frenamos already tells you the subject is we, and Spanish does not need nosotros unless the speaker wants emphasis or contrast.

Compare:

• Más fuerte frenamos. = normal
• Más fuerte frenamos nosotros. = more emphatic, like we are the ones who brake harder

Because the sentence expresses a general rule, habit, or regular relationship.

Spanish often uses the present tense for this, just like English does:

• The faster the bicycle goes, the harder we brake.
• Cuanto más rápido va la bicicleta, más fuerte frenamos.

It is not necessarily talking about one specific moment. It is describing what generally happens.

If you wanted a past situation, the tenses would change:

• Cuanto más rápido iba la bicicleta, más fuerte frenábamos.
• The faster the bicycle was going, the harder we were braking.

No, frenar can be used intransitively.

That means it can mean simply to brake without stating a direct object.

So:

• Frenamos. = We brake / We apply the brakes.

It can also be transitive in other contexts:

• Frenamos la bicicleta. = We braked the bicycle / slowed the bicycle down.

But in your sentence, no object is necessary.

Because in Spanish, a singular count noun usually needs some kind of determiner, such as:

• el / la
• un / una
• a possessive like mi
• a demonstrative like esta

So bicicleta by itself would usually not work as the subject here.

That is why you get:

• la bicicleta

In context, this can mean:

• a specific bicycle being discussed
• or the bicycle in a general, representative sense

Yes, in many parts of Latin America, you may hear alternatives such as:

• Mientras más rápido va la bicicleta, más fuerte frenamos.
• Entre más rápido va la bicicleta, más fuerte frenamos.

These forms are common in various regions.

However, cuanto más... is a very standard and widely accepted option, and many textbooks prefer it as the safest general pattern.

So for a learner:

• cuanto más... = excellent standard choice
• mientras más... / entre más... = common regional alternatives

It is understandable and basically natural. Still, depending on context, a native speaker might choose a slightly different version.

For example:

• Cuanto más rápido va la bicicleta, más fuerte frenamos.
• Cuanto más rápido va la bicicleta, con más fuerza frenamos.
• Cuanto más rápido va la bicicleta, más fuerte hay que frenar.

The last one can sound more natural if the meaning is general advice, because it means something like:

• The faster the bicycle goes, the harder you have to brake.

So your original sentence is fine, but native speakers might adjust it depending on whether they mean:

• we specifically
• people in general
• or an instruction/advice statement