الخفاقة قرب الملعقة الخشبية.

In Arabic, the present-tense to be is usually not expressed.

So:

الخفاقة قرب الملعقة الخشبية
literally looks like: the whisk near the wooden spoon

but it means: The whisk is near the wooden spoon.

This is a very normal Arabic sentence pattern, called a nominal sentence. If you wanted a past or future meaning, then Arabic would use a verb such as كان.

Here, قرب means near or close to.

Grammatically, it is often treated as an adverbial expression of place or a noun used adverbially:
قربَ الملعقةِ = near the spoon

So the sentence is built like this:

• الخفاقة = the whisk
• قرب الملعقة الخشبية = near the wooden spoon

Together: The whisk is near the wooden spoon.

Because قرب can be used in an iḍāfa-like construction directly with the following noun:

• قربَ الملعقةِ = near the spoon

Arabic also has other very common ways to say the same idea, such as:

• بالقرب من الملعقة الخشبية
• قريبة من الملعقة الخشبية

So the sentence you have is correct, but it is not the only possible phrasing.

Because Arabic adjectives usually come after the noun they describe.

So:

• الملعقة = the spoon
• الخشبية = the wooden

Together:

• الملعقة الخشبية = the wooden spoon

This is the normal Arabic order: noun + adjective.

Because it must agree with الملعقة, which is a feminine singular noun.

Arabic adjectives agree with the noun in:

• gender
• number
• definiteness
• case

So since الملعقة is feminine singular, the adjective must also be feminine singular:

• خشبي = wooden, masculine
• خشبية = wooden, feminine

That is why you get:

• الملعقة الخشبية

not الملعقة الخشبي.

Because adjectives in Arabic also agree with the noun in definiteness.

Since the noun is definite:

• الملعقة = the spoon

the adjective must also be definite:

• الخشبية = the wooden

So:

• الملعقة الخشبية literally = the spoon the wooden
• natural English translation = the wooden spoon

If the noun were indefinite, the adjective would also be indefinite.

Because both are definite in the meaning of the sentence:

• الخفاقة = the whisk
• الملعقة الخشبية = the wooden spoon

Arabic marks definiteness very clearly with الـ. Since the meaning here is not a whisk or a wooden spoon, but specific known items, the definite article appears.

With full vowels, the sentence would be:

الخَفّاقةُ قُرْبَ المِلْعَقَةِ الخَشَبِيَّةِ

Here is why:

• الخَفّاقةُ: nominative, because it is the subject/topic
• قُرْبَ: accusative as an adverbial expression of place
• المِلْعَقَةِ: genitive after قرب in this construction
• الخَشَبِيَّةِ: genitive too, because it agrees with المِلعقة

In normal Arabic writing, these short vowels are usually not written.

A helpful pronunciation is:

al-khaffāqa qurb al-mil‘aqa al-khashabiyya

If you pronounce it with full case endings, it is closer to:

al-khaffāqatu qurb al-mil‘aqati al-khashabiyyati

A few sounds to notice:

• خ = a throaty kh sound
• ع in ملعقة = the Arabic ʿayn, a consonant that English does not have
• ة at the end of words like خفاقة and ملعقة is usually pronounced -a in pause

No. Arabic has several natural ways to express this idea. For example:

• الخفاقة قرب الملعقة الخشبية
• الخفاقة قريبة من الملعقة الخشبية
• الخفاقة بالقرب من الملعقة الخشبية
• الخفاقة بجانب الملعقة الخشبية

They are all close in meaning, though the style and structure differ a little. For a learner, قريبة من is often the easiest to recognize, while قرب is compact and common in formal Arabic.