Die Katze hebt eine Pfote, als ob sie uns begrüßen wollte.

Katze is a feminine noun in German, so its dictionary article is die.

In this sentence, die Katze is also the subject of the sentence, so it is in the nominative case:

• die Katze = the cat

So die here tells you both:

• the noun is feminine
• it is the subject

Eine Pfote is the direct object of hebt.

The verb heben means to lift / to raise, and the thing being lifted is the object:

• The cat raises a paw.

That is why Pfote is in the accusative case.

With feminine nouns, the article eine looks the same in both nominative and accusative:

• nominative: eine Pfote
• accusative: eine Pfote

So the form does not change, even though the function does.

Hebt is the 3rd person singular present tense of heben.

• heben = to lift / to raise
• sie hebt = she/it lifts, raises

Here it describes what the cat is doing right now or in the scene being described:

• Die Katze hebt eine Pfote = The cat raises/lifts a paw

Because als ob introduces a subordinate clause.

In German, subordinate clauses are normally separated from the main clause with a comma:

• Die Katze hebt eine Pfote, als ob ...

This is a very standard punctuation rule in German.

Als ob means as if or as though.

It introduces a comparison that is often:

• imagined
• uncertain
• only apparently true

So the sentence means the cat raises a paw as if it wanted to greet us.

German often uses als ob for situations that are not stated as fact, but only as an impression.

Because als ob starts a subordinate clause, and in German subordinate clauses the finite verb usually goes to the end.

So instead of a main-clause order like:

• sie wollte uns begrüßen

you get:

• als ob sie uns begrüßen wollte

The order is:

• sie = subject
• uns = object
• begrüßen = infinitive
• wollte = finite verb at the end

This is very common with subordinate clauses in German.

Because wollte is the finite verb of the subordinate clause, and finite verbs go to the end in clauses introduced by als ob.

So:

• main clause: Die Katze hebt eine Pfote
• subordinate clause: als ob sie uns begrüßen wollte

Also, since wollen is a modal verb, the other verb (begrüßen) stays in the infinitive, and the modal verb comes last in the clause.

Not really in the normal time sense.

This is one of the trickier parts. Wollte can be:

• simple past of wollen
• or Konjunktiv II of wollen

The forms are identical.

In this sentence, because of als ob, learners should usually understand wollte as expressing an unreal or apparent situation:

• as if she wanted to greet us

So it does not mean that the wanting happened in the past. It is more about appearance or impression.

Because wollen is a modal verb, and modal verbs are followed by a bare infinitive in German.

So you say:

• sie wollte uns begrüßen

not:

• sie wollte uns zu begrüßen

This is the same pattern as with other modal verbs such as:

• kann kommen
• muss gehen
• darf bleiben

Begrüßen means to greet, and uns is the object pronoun meaning us.

So:

• jemanden begrüßen = to greet someone
• uns begrüßen = to greet us

Uns is in the accusative case, because begrüßen takes a direct object.

Grammatically, sie refers back to die Katze, because Katze is feminine.

So in German:

• die Katze ... sie

In English, you might translate that as:

• she, if the cat is being personified or known to be female
• it, if you are speaking more neutrally

So the German pronoun follows grammatical gender, not necessarily the exact English choice.

Yes. A very common alternative is:

• Die Katze hebt eine Pfote, als wollte sie uns begrüßen.

This is a shorter version without ob, and it means essentially the same thing:

• The cat raises a paw, as if it wanted to greet us.

Both are correct.
The version with als ob may feel a little more explicit for learners, because the clause structure is easier to recognize.