Ich mache mein Fahrrad mit dem Fahrradschloss am Zaun fest.

Because festmachen is a separable verb.

The full verb is festmachen, which often means to fasten, to attach, or to secure. In a normal present-tense main clause, the verb splits:

• Ich mache ... fest.

So:

• machen goes to the usual verb position
• fest goes to the end of the clause

This is very common in German with separable verbs, for example:

• Ich stehe um 7 Uhr auf.
• Er ruft seine Mutter an.

In an infinitive, the verb stays together:

• Ich will mein Fahrrad am Zaun festmachen.

Festmachen is the key verb in this sentence. Here it means something like:

• to fasten
• to secure
• to lock up / attach securely

So Ich mache mein Fahrrad ... fest means that the speaker is securing the bike so it cannot easily be moved away.

It is often used for physically attaching one thing to another. You may also hear it with boats:

• Das Boot am Steg festmachen = to tie up the boat at the dock

Because Fahrrad is the direct object here, and it is neuter: das Fahrrad.

The verb festmachen takes a direct object: what is being secured?
Answer: mein Fahrrad

In the accusative case, the forms are:

• masculine: meinen
• feminine: meine
• neuter: mein
• plural: meine

Since Fahrrad is neuter, the correct form is:

• mein Fahrrad

Compare:

• Ich sehe meinen Bruder.
• Ich sehe meine Schwester.
• Ich sehe mein Fahrrad.

Because mit always takes the dative case.

So:

• das Fahrradschloss becomes dem Fahrradschloss

That part means with the bike lock.

This is a very important pattern:

• mit dem Auto
• mit der Tasche
• mit einem Freund

So in this sentence:

• mit dem Fahrradschloss = with the bike lock

Because here the sentence describes location, not direction toward a place.

The preposition an can take either:

• dative for location
• accusative for movement toward something

Here, the bike is being secured at/on the fence, so German treats that as location:

• an dem Zaun → am Zaun

Compare:

• Ich hänge das Bild an die Wand.
  movement toward the wall → accusative

• Das Bild hängt an der Wand.
  location on the wall → dative

In your sentence, the bike ends up attached at the fence, so:

• am Zaun = an dem Zaun

Am is a contraction of:

• an dem

So:

• am Zaun = an dem Zaun

German often contracts certain preposition + article combinations:

• an dem → am
• in dem → im
• zu dem → zum
• zu der → zur

These contractions are extremely common and usually sound more natural than the full forms.

Because two different parts of the sentence require the dative:

1. mit dem Fahrradschloss
   because mit always takes dative

2. am Zaun = an dem Zaun
   because an takes dative here when it expresses location

So both nouns happen to be in the dative:

• dem Fahrradschloss
• dem Zaun

This does not mean they have the same function. They are different prepositional phrases:

• mit dem Fahrradschloss = the means/instrument
• am Zaun = the place where it is secured

Yes, exactly.

You can think of the sentence like this:

• Ich mache mein Fahrrad = what I do
• mit dem Fahrradschloss = what I use to do it
• am Zaun = where I secure it

So:

• mit dem Fahrradschloss answers With what?
• am Zaun answers Where?

This is a very helpful way to understand German prepositional phrases.

Yes. German word order is flexible, especially with adverbial and prepositional phrases.

The sentence you have is completely natural:

• Ich mache mein Fahrrad mit dem Fahrradschloss am Zaun fest.

But you could also say:

• Ich mache mein Fahrrad am Zaun mit dem Fahrradschloss fest.

Both are grammatical. The difference is mostly one of emphasis or style.

German usually keeps the conjugated verb in second position and the separable prefix at the end, but the material in the middle can often move around.

Because German often uses different verbs depending on the exact idea.

• festmachen focuses on fastening/securing something to something
• abschließen often focuses on locking something
• anschließen can mean to lock/chain something to something in some contexts

Your sentence uses festmachen, which fits well because the bike is being secured with a lock to the fence.

A learner may also hear:

• Ich schließe mein Fahrrad am Zaun ab.
• Ich schließe mein Fahrrad an den Zaun an.

These are related ideas, but the chosen sentence specifically uses festmachen.

Yes. Fahrradschloss is a compound noun, which is extremely common in German.

It combines:

• Fahrrad = bicycle
• Schloss = lock

So:

• Fahrradschloss = bicycle lock / bike lock

The last part usually determines the grammatical gender, and Schloss is neuter:

• das Schloss
• therefore das Fahrradschloss

German makes compounds very freely, which is why long nouns are so common.

They are in different cases because they play different roles.

• mein Fahrrad = accusative
  It is the direct object: the thing being secured.

• dem Fahrradschloss = dative
  It follows mit, which requires dative.

• am Zaun = dative
  It comes from an dem Zaun, and an takes dative here because it expresses location.

So the sentence contains:

• one accusative noun phrase
• two dative prepositional phrases

Then the separable verb festmachen stays together at the end.

For example:

• Ich will mein Fahrrad mit dem Fahrradschloss am Zaun festmachen.
• Ich muss mein Fahrrad mit dem Fahrradschloss am Zaun festmachen.

That is because after a modal verb, the main verb appears in the infinitive form, and separable verbs are not split in the infinitive.

Usually yes, or at least attached to it in a practical sense.

An often suggests being at, on, or attached to a vertical surface or object. With a fence, am Zaun usually means the bike is secured to the fence, not just somewhere nearby.

If you wanted to say merely near the fence, you would more likely use:

• beim Zaun
• neben dem Zaun
• or another expression depending on the situation

So am Zaun is a good choice for a bike locked to a fence.

Yes, it is natural and understandable German.

That said, in everyday speech many speakers might also choose a verb more specifically connected with locks, such as:

• Ich schließe mein Fahrrad am Zaun ab.

But the given sentence is perfectly normal, especially if the focus is on fastening/attaching the bike securely with a lock.

So for a learner, the sentence is useful because it teaches several important things at once:

• a separable verb
• dative after mit
• dative with an for location
• compound nouns
• flexible word order in the middle of the sentence