Da der Wäscheständer voll ist, hängt meine Mutter die Socken mit einer Wäscheklammer an den Balkonstuhl.

No. In this sentence, da does not mean there. It means since or because.

So:

• Da der Wäscheständer voll ist, ... = Since/Because the drying rack is full, ...

This da is a conjunction that introduces a reason.

A learner might compare it with weil:

• Da der Wäscheständer voll ist, hängt ...
• Weil der Wäscheständer voll ist, hängt ...

Both can mean because, but da often sounds a bit more formal or is used when the reason is already known or taken as background information.

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

So the clause is structured like this:

• Da = subordinating conjunction
• der Wäscheständer = subject
• voll = predicate adjective
• ist = verb at the end

This is a very common German pattern:

• weil er müde ist
• dass sie keine Zeit hat
• obwohl es regnet

So Da der Wäscheständer voll ist follows the normal subordinate-clause word order.

Because the sentence starts with the subordinate clause.

German main clauses follow the verb-second rule. That means the conjugated verb must come in the second position. If the first position is taken by a whole subordinate clause, then the verb comes immediately after that clause.

Structure:

1. Da der Wäscheständer voll ist = first position
2. hängt = verb in second position
3. meine Mutter = subject

So:

• Da der Wäscheständer voll ist, hängt meine Mutter die Socken ...

If you start with the main clause instead, then you get:

• Meine Mutter hängt die Socken an den Balkonstuhl, da der Wäscheständer voll ist.

Both are correct.

Der Wäscheständer is in the nominative case because it is the subject of the subordinate clause:

• der Wäscheständer = the drying rack
• ist voll = is full

The noun Wäscheständer is masculine, so in the nominative singular it takes der:

• nominative: der Wäscheständer
• accusative: den Wäscheständer
• dative: dem Wäscheständer
• genitive: des Wäscheständers

Here it is the thing that is full, so nominative is needed.

Here die Socken is accusative, because it is the direct object of hängt:

• Who is doing the action? meine Mutter
• What is she hanging? die Socken

The tricky part is that for plural nouns, nominative and accusative often look the same:

• nominative plural: die Socken
• accusative plural: die Socken

So you can only tell from the function in the sentence. Here it is the object, so it is accusative.

Because the preposition mit always takes the dative case.

So:

• nominative: eine Wäscheklammer
• accusative: eine Wäscheklammer
• dative: einer Wäscheklammer

That is why the sentence says:

• mit einer Wäscheklammer = with a clothespin

This is a good preposition to memorize with dative from the start:

• mit dem Auto
• mit meiner Schwester
• mit einer Wäscheklammer

Because an is a two-way preposition. With two-way prepositions, German uses:

• accusative for direction or destination
• dative for location

Here the socks are being hung onto the balcony chair, so there is a sense of placement/direction. That is why German uses the accusative:

• an den Balkonstuhl

Compare:

• Die Socken hängen an dem Balkonstuhl.
  = The socks are hanging on the balcony chair.
  → location, so dative

• Meine Mutter hängt die Socken an den Balkonstuhl.
  = My mother hangs the socks onto the balcony chair.
  → placement/direction, so accusative

Because an is commonly used when something is attached, hung, or placed against a vertical surface or edge.

Here the idea is that the socks are clipped to the chair, not simply lying on top of it.

Very roughly:

• an = on, at, attached to, against
• auf = on top of

So:

• an den Balkonstuhl hängen suggests fastening the socks to the chair
• auf den Balkonstuhl legen would mean putting them on top of the chair

With hanging and clothespins, an is the natural choice.

Here it means to hang something — the transitive use.

German hängen can be confusing because there are two common patterns:

1. transitive: to hang something

   • Ich hänge die Jacke an die Tür.
   • I hang the jacket on the door.

2. intransitive: to be hanging

   • Die Jacke hängt an der Tür.
   • The jacket is hanging on the door.

In your sentence:

• meine Mutter hängt die Socken ...
• She is actively hanging the socks.

So this is the transitive use, with die Socken as a direct object.

Grammatically, singular is perfectly fine. The sentence simply says she hangs the socks with a clothespin.

German often uses the singular when mentioning a tool or means in a general way:

• mit einem Messer = with a knife
• mit einem Stift = with a pen
• mit einer Wäscheklammer = with a clothespin

It does not necessarily mean there is only one clothespin in the whole situation; it is just how the action is being described here.

Of course, a different sentence could say:

• mit Wäscheklammern = with clothespins
• mit zwei Wäscheklammern = with two clothespins

They are compound nouns, which are extremely common in German.

You can often understand them by splitting them up:

• Wäsche = laundry

• Ständer = stand/rack
  → Wäscheständer = laundry rack / drying rack

• Wäsche = laundry
• Klammer = clip → Wäscheklammer = clothespin / laundry clip

A very useful rule:

• In German compounds, the last part determines the gender.

So:

• der Ständer → der Wäscheständer
• die Klammer → die Wäscheklammer
• der Stuhl → der Balkonstuhl

This rule helps a lot with article learning.

Yes. Balkonstuhl is a compound noun:

• Balkon = balcony
• Stuhl = chair

So Balkonstuhl means balcony chair.

And again, the last element determines the gender:

• der Stuhl → der Balkonstuhl

That is why you get:

• nominative: der Balkonstuhl
• accusative: den Balkonstuhl

Which explains:

• an den Balkonstuhl

Yes, you usually can:

• Weil der Wäscheständer voll ist, hängt meine Mutter die Socken mit einer Wäscheklammer an den Balkonstuhl.

That is grammatical and natural.

The main differences are nuance and style:

• weil is the most common everyday word for because
• da often sounds a bit more literary, formal, or background-setting

In many contexts, both work. A learner should mainly remember that both da and weil send the verb to the end of the clause they introduce.

Yes, German word order is flexible, but not random.

In this sentence:

• die Socken = direct object
• mit einer Wäscheklammer = manner/instrument
• an den Balkonstuhl = destination/location of placement

This order is very natural. But German can move these elements around for emphasis:

• ... hängt meine Mutter die Socken an den Balkonstuhl.
• ... hängt meine Mutter die Socken mit einer Wäscheklammer an den Balkonstuhl.
• ... hängt meine Mutter mit einer Wäscheklammer die Socken an den Balkonstuhl.

Some versions sound more natural than others depending on context. The original sentence is a normal, clear choice.

For learners, the important thing is:

• the verb stays in second position in the main clause
• the other elements can sometimes move, especially for emphasis

Then German would normally use the location pattern instead of the placement pattern.

Compare:

Placement/action

• Meine Mutter hängt die Socken an den Balkonstuhl.
• She hangs the socks onto the balcony chair.

Location/result

• Die Socken hängen an dem Balkonstuhl.
• The socks are hanging on the balcony chair.

Notice two changes:

1. The verb meaning changes from hang something to be hanging
2. an takes dative for location:
   • an dem Balkonstuhl

This is a very important pattern in German with two-way prepositions.