عمود الخدش قرب الباب.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is / am / are.

So عمود الخدش قرب الباب naturally means The scratching post is near the door without needing an explicit verb.

If you wanted a past-tense version, you would use a verb such as كان:

• كان عمود الخدش قرب الباب = The scratching post was near the door

Yes. It is an iḍāfa construction, often called a genitive or possessive construction.

Here:

• عمود = post / pillar / pole
• الخدش = scratching / scratch

So literally it is something like post of scratching, which English would normally express as scratching post.

In an iḍāfa:

• the first noun is the thing being described: عمود
• the second noun specifies it: الخدش

Because in an iḍāfa, the first noun normally does not take الـ.

Definiteness is determined by the second noun:

• عمود الخدش = the scratching post
• عمود خدش = a scratching post or just scratching post

So even though عمود has no الـ, the whole phrase can still be definite because الخدش is definite.

Also, the first noun in iḍāfa does not take tanwīn.

No, here الخدش is a noun, not a verb.

More specifically, it is a verbal noun or maṣdar, meaning something like:

• scratching
• a scratch
• abrasion

So in this sentence it functions as the second noun in the iḍāfa: عمود الخدش.

قرب here means near.

In traditional grammar, it is often treated as a ẓarf or adverbial noun of place, though for learners it is often easiest to think of it as working a lot like a preposition.

So:

• قرب الباب = near the door

The noun after it, الباب, is in the genitive case.

Because it comes after قرب.

So in a fully vocalized version, you would have:

• البابِ

That final kasra shows the genitive.

This is very common after words that function like prepositions or adverbial location words.

A fully vocalized version would be:

عَمُودُ الخَدْشِ قُرْبَ البَابِ

Here is why:

• عَمُودُ: nominative, because it is the subject/topic of the nominal sentence
• الخَدْشِ: genitive, because it is the second term of the iḍāfa
• قُرْبَ: accusative, because it is a ẓarf of place
• البَابِ: genitive, because it follows قرب

In normal writing, these short vowels are usually omitted.

Yes. Arabic word order is somewhat flexible.

The sentence as given:

• عمود الخدش قرب الباب

is a neutral way to say The scratching post is near the door.

You could also say:

• قرب الباب عمود الخدش

This puts more focus on the location, something like Near the door is the scratching post.

Both are possible, but the original order is straightforward and natural.

These are the main tricky sounds:

• ع in عمود: a deep throat sound. English does not really have it.
• خ in الخدش: like the ch in German Bach or Scottish loch
• ق in قرب: a deep k/q sound made farther back in the mouth than English k

A rough learner-friendly transliteration is:

ʿamūd al-khadsh qurb al-bāb

Not perfect, but useful as a starting point.

They are close in meaning, but not always identical.

• قرب الباب = near the door
• بجانب الباب = beside / next to the door

So بجانب can sound a bit more specifically like right beside, while قرب can be slightly broader.

They mean very different things:

• عمود الخدش = scratching post or literally post for scratching
• العمود المخدوش = the scratched post

So:

• الخدش is a noun in an iḍāfa
• المخدوش is an adjective/passive participle meaning scratched

This is a very common kind of distinction in Arabic.