عود الثقاب قرب الشمعة.

Because Arabic often uses a nominal sentence in the present tense, with no spoken or written verb for is/are.

So:

عود الثقاب قرب الشمعة
literally looks like matchstick near the candle,
but naturally means The matchstick is near the candle.

If you wanted a different tense, then Arabic would usually add a verb, for example:

كان عودُ الثقابِ قربَ الشمعةِ = The matchstick was near the candle.

It is an iḍāfa (construct phrase), a very common Arabic structure.

• عود = stick
• الثقاب = matches / the match

Together, عود الثقاب means the matchstick or literally the stick of the match(es).

In Arabic, many everyday noun combinations are built this way.

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

The definiteness of the whole phrase is determined by the second noun:

• عودُ الثقابِ = the matchstick
• عودُ ثقابٍ = a matchstick

So even without الـ on عود, the whole phrase can still be definite.

Here قرب is best understood as a noun used adverbially, meaning nearness or in the vicinity of. In practice, it functions like near.

So:

قرب الشمعة = near the candle

This is slightly different from the adjective قريب:

• قرب الشمعة = near the candle
• قريب من الشمعة = close to the candle

Both are possible, but they are built differently.

Because قرب in this sentence is not behaving like قريب.

Compare the two patterns:

• قربَ الشمعةِ = near the candle
• قريبٌ من الشمعةِ = close to the candle

So:

• قرب usually takes the following noun directly in an iḍāfa-like structure
• قريب usually uses من

That is why the sentence does not say قرب من الشمعة.

A fully vocalized version would be:

عُودُ الثِّقابِ قُرْبَ الشَّمْعَةِ

The grammar is:

• عُودُ — nominative, because it is the subject/topic of the nominal sentence
• الثِّقابِ — genitive, because it is the second term of the iḍāfa
• قُرْبَ — accusative, because it is an adverbial expression of place
• الشَّمْعَةِ — genitive, because it is linked to قرب in another construct-like relation

In normal unvocalized Arabic writing, these endings are usually not written.

It is the predicate of the nominal sentence.

So the sentence divides like this:

• عود الثقاب = the topic / subject
• قرب الشمعة = the predicate, telling you where it is

In English, the predicate would be is near the candle.
In Arabic, the location phrase itself can serve as the predicate.

Yes. Arabic allows more flexibility than English.

The given order:

عود الثقاب قرب الشمعة
is a straightforward way to say it.

But Arabic can also front the location for emphasis, for example:

قرب الشمعة عودُ الثقابِ

That would mean something like Near the candle is the matchstick or The matchstick is near the candle, with more focus on the location.

For a learner, the original order is a good neutral pattern to follow.

Because ث and ش are both sun letters.

When الـ comes before a sun letter, the l sound is not pronounced; instead, the following consonant is doubled.

So:

• الثقاب is pronounced roughly ath-thiqāb
• الشمعة is pronounced roughly ash-shamʿa

This happens in pronunciation, but the spelling still keeps الـ.

In this expression, the whole phrase عود ثقاب refers to one matchstick.

So:

• عودُ ثقابٍ = a matchstick
• عودُ الثقابِ = the matchstick

The word ثقاب can refer to matches as a general item or category, and Arabic often uses this kind of noun combination for single objects.

If you want a clear plural, you might say something like:

أعواد ثقاب = matchsticks

Yes. Arabic has several common alternatives, for example:

• قرب الشمعة = near the candle
• بالقرب من الشمعة = near the candle / close to the candle
• عند الشمعة = by the candle / at the candle
• بجانب الشمعة = beside the candle
• قريب من الشمعة = close to the candle

The sentence you were given is short and natural, especially in simple descriptive Arabic.