Der Kratzer an der Tür ist schon alt.

Kratzer is a masculine noun, so its basic article is der: der Kratzer.

There is not always a reliable rule from the word ending alone, so in many cases you simply need to learn the noun together with its article:

• der Kratzer = the scratch
• die Tür = the door

A very good habit is to memorize German nouns with their article from the start, not as separate vocabulary items.

Because this sentence describes a location, not a direction of movement.

The preposition an can take either:

• dative for location: an der Tür = on/at the door
• accusative for movement toward something: an die Tür = to the door

So:

• Der Kratzer an der Tür = the scratch on the door
• Ich male einen Kreis an die Tür = I paint a circle onto the door

Here, the scratch is simply located on the door, so German uses the dative: an der Tür.

Because Tür is a feminine noun, and after an in a location meaning, it must be in the dative case.

For a feminine noun:

• nominative: die Tür
• dative: der Tür

So:

• die Tür = the door
• an der Tür = on/at the door

This is one of the most common things English speakers notice in German: the article changes to show case.

German main clauses normally follow the verb-second rule, often called V2. That means the finite verb comes in the second position.

In this sentence:

• Der Kratzer an der Tür = first element
• ist = second element
• schon alt = the rest

So the structure is normal German word order.

You can think of it as:

• [The scratch on the door] [is] [already old]

Because alt is used here as a predicate adjective, after the verb sein.

In German:

• adjectives before a noun usually take endings:
  der alte Kratzer
• adjectives after sein, werden, bleiben usually do not take endings:
  Der Kratzer ist alt

So:

• der alte Kratzer = the old scratch
• Der Kratzer ist alt = the scratch is old

That is why alt stays in its basic form here.

Here schon means something like already, by now, or as it is.

So schon alt suggests:

• the scratch is not new
• it has been there for some time
• maybe it should not be surprising anymore

Depending on tone and context, schon can add a small nuance, for example:

• Der Kratzer ist alt. = The scratch is old.
• Der Kratzer ist schon alt. = The scratch is already old / has been there a while.

Literally, an can often mean at, on, or by, depending on context.

In this sentence, because we are talking about a scratch, the natural English meaning is on the door.

So although an der Tür can sometimes be translated in other ways in other contexts, here you should understand it as:

• the scratch on the door

German often uses definite articles where English also would, especially when talking about a specific thing in a specific context.

Here:

• der Kratzer = a particular scratch
• der Tür = a particular door

Even if English might sometimes sound okay with slightly different choices in other contexts, this sentence is completely normal German. The speaker is referring to a specific scratch associated with a specific door.

Sometimes learners wonder about an versus auf.

In this sentence, an der Tür is the natural choice for something located on the surface of a vertical object like a door or wall.

auf der Tür is usually less natural here and may sound odd, or it may suggest something more like on top of the door, depending on context.

So for a scratch on the surface of a door, an der Tür is the better choice.

Yes. The core noun is der Kratzer, and an der Tür is a prepositional phrase that describes which scratch we mean.

So the full subject noun phrase is:

• Der Kratzer an der Tür = the scratch on the door

Then the rest of the sentence tells us something about that subject:

• ist schon alt = is already old

It describes the scratch, not the door.

The subject of the sentence is Der Kratzer an der Tür, and the predicate ist schon alt tells us something about that subject.

So the meaning is:

• the scratch is old

If you wanted to say the door is old, you would need a different sentence, such as:

• Die Tür ist alt.

They are similar, but not always exactly the same.

• Kratzer usually means a scratch or scrape mark, often on a surface
• Schramme can mean a scrape, often on skin, but it can also be used more generally

In this sentence, Kratzer is a very natural word for a mark on a door.