Auf dem Sofa schnurrt unsere alte Katze so laut, dass meine Tochter lachen muss.

German often puts a location or time expression first for emphasis or style. Here, Auf dem Sofa is in the first position, so the conjugated verb must come next:

• Auf dem Sofa = first element
• schnurrt = second position
• unsere alte Katze = subject after the verb

This is a standard verb-second pattern in German main clauses.

Compare:

• Unsere alte Katze schnurrt auf dem Sofa.
• Auf dem Sofa schnurrt unsere alte Katze.

Both are correct, but the second one emphasizes the location a bit more.

Because auf can take either the accusative or the dative, depending on meaning.

Here it describes a location: the cat is already on the sofa, not moving onto it. For location, German uses the dative:

• auf dem Sofa = on the sofa

If there were movement toward the sofa, you would use accusative:

• Die Katze springt auf das Sofa. = The cat jumps onto the sofa.

Also, Sofa is neuter (das Sofa), and the dative singular form of das is dem.

schnurrt means purrs.

Its infinitive is schnurren = to purr.

This is the 3rd person singular form, used with unsere alte Katze:

• ich schnurre
• du schnurrst
• er/sie/es schnurrt

So:

• unsere alte Katze schnurrt = our old cat purrs

Both unsere and alte are describing Katze, which is a feminine singular noun.

Here, Katze is the subject of the sentence, so it is in the nominative case.

That gives:

• unsere = our
• alte = old
• Katze = cat

So the phrase is:

• unsere alte Katze = our old cat

This is a normal pattern for feminine singular nominative after a possessive word like unser.

Because laut here is an adverb, not an adjective directly describing a noun.

It modifies the verb schnurrt:

• schnurrt laut = purrs loudly

Adverbs in German do not take adjective endings.

Compare:

• eine laute Katze = a loud cat
  
  • here laute is an adjective describing Katze
• Die Katze schnurrt laut. = The cat purrs loudly
  
  • here laut is an adverb

so ..., dass ... means so ... that ...

It introduces a result:

• so laut = so loudly
• dass meine Tochter lachen muss = that my daughter has to laugh / can't help laughing

So the sentence shows cause and result:

• the cat purrs so loudly
• that the daughter laughs

This is a very common German structure:

• Er ist so müde, dass er einschläft. = He is so tired that he falls asleep.
• Sie spricht so schnell, dass ich sie kaum verstehe. = She speaks so fast that I can hardly understand her.

Because dass introduces a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

So:

• main clause: Auf dem Sofa schnurrt unsere alte Katze so laut
• subordinate clause: dass meine Tochter lachen muss

Inside that subordinate clause:

• meine Tochter = subject
• lachen muss = verb phrase at the end

With a modal verb, the infinitive and the modal stay together at the end:

• ... dass meine Tochter lachen muss.

In a normal main clause, you would often say:

• Meine Tochter muss lachen.

But after dass, the clause becomes subordinate, so the verb moves to the end:

• ..., dass meine Tochter lachen muss.

So both forms are correct, but they belong to different clause types:

• main clause: muss lachen
• subordinate clause: lachen muss

Literally, yes: must laugh.

But in many contexts it is more natural in English to translate it as:

• has to laugh
• can’t help laughing
• has to burst out laughing (depending on context)

In this sentence, it probably does not mean that the daughter is forced by obligation to laugh. It means the cat purrs so loudly that she naturally starts laughing.

Because meine Tochter is the subject of the subordinate clause, so it is in the nominative case.

• meine Tochter = my daughter

You would see meiner Tochter in dative contexts, for example:

• Ich gebe meiner Tochter ein Buch. = I give my daughter a book.

But here, your daughter is the one doing the laughing, so nominative is correct:

• dass meine Tochter lachen muss

Usually yes in a sentence like this.

But it helps to understand the core idea rather than memorize one fixed translation:

• auf often means on
• with dative, it often expresses location

So here:

• auf dem Sofa = on the sofa

In other contexts, English might phrase things a little differently, but on the sofa is the natural translation here.

Yes. German word order is flexible, as long as the grammar rules are respected.

For example:

• Unsere alte Katze schnurrt auf dem Sofa so laut, dass meine Tochter lachen muss.

This has a more neutral feel because the subject comes first.

The original version:

• Auf dem Sofa schnurrt unsere alte Katze so laut, dass meine Tochter lachen muss.

puts more attention on where the action is happening.

Both are correct. The choice is about emphasis and style, not basic meaning.