Nach der Reparatur richten wir Sattel und Lenker aus.

Because nach takes the dative case when it means after.

• nominative: die Reparatur
• dative: der Reparatur

So:

• nach der Reparatur = after the repair

This is a very common pattern:

• nach dem Essen = after the meal
• nach der Arbeit = after work

German main clauses follow the V2 rule: the finite verb must be in the second position.

Here, Nach der Reparatur takes the first position, so the verb must come next:

• Nach der Reparatur | richten | wir ...

Even though Nach der Reparatur is several words, it counts as one unit in first position.

You could also say:

• Wir richten nach der Reparatur Sattel und Lenker aus.

That is also grammatical, but it puts less emphasis on the time expression.

Because ausrichten is a separable verb.

Its full infinitive is:

• ausrichten

In a main clause, German separates it:

• richten ... aus

So:

• Wir richten Sattel und Lenker aus.

This is very common with separable verbs:

• Ich kaufe ein. from einkaufen
• Er steht auf. from aufstehen

The dictionary form is ausrichten.

When you look it up, you look under ausrichten, not under richten.

In this sentence, ausrichten means something like to align, to adjust, or to straighten into the correct position.

Be aware that ausrichten can have other meanings in other contexts, so context matters.

They are in the accusative case because they are the direct objects of ausrichten.

We are aligning what?

• Sattel
• Lenker

Both nouns are masculine:

• der Sattel
• der Lenker

If the articles were included, the accusative forms would be:

• den Sattel
• den Lenker

This is a good question, because learners often expect:

• den Sattel und den Lenker

And that version is also perfectly natural.

The version without articles can sound a bit more technical, general, or workshop-style, as if describing a standard service procedure rather than focusing on one specific bike part as an individual object.

So both ideas are possible:

• Nach der Reparatur richten wir Sattel und Lenker aus.
  slightly more general / technical / service-description style

• Nach der Reparatur richten wir den Sattel und den Lenker aus.
  very natural when talking about one specific bicycle

As a learner, if you are unsure, using the articles is often the safer choice.

Because German normally uses der Lenker as a singular noun for the whole handlebar unit.

So:

• der Lenker = the handlebar(s)

This is one of those places where German and English package the object differently.

Similarly:

• English: glasses
• German: die Brille (singular)

So even if English prefers a plural word, German may use a singular one.

Yes, but only if you change the structure.

• nach is followed by a noun phrase:

  • nach der Reparatur

• nachdem introduces a subordinate clause:

  • Nachdem wir das Fahrrad repariert haben, richten wir den Sattel und den Lenker aus.

So:

• nach der Reparatur = after the repair
• nachdem wir ... repariert haben = after we have repaired ...

Both can express the same basic idea, but the grammar is different.

Because all German nouns are capitalized.

In this sentence, the nouns are:

• Reparatur
• Sattel
• Lenker

This is one of the most visible spelling differences between German and English.

Not really.

By itself, richten has other meanings, such as to direct, to judge, or in some contexts to set/arrange. In this bicycle context, ausrichten is the natural verb for aligning something into the correct position.

So here, the aus- is important. It gives the technical sense of getting something properly lined up.