عود الثقاب قرب الشمعة، والماس الكهربائي قرب القابس.

Because Arabic usually omits the present-tense verb to be in simple statements.

So:

• عود الثقاب قرب الشمعة = The matchstick is near the candle
• الماس الكهربائي قرب القابس = The electrical short/contact is near the plug/socket

This is called a nominal sentence in Arabic. In the present tense, Arabic normally just puts:

• the thing being talked about
• plus the information about it

If you wanted was, will be, etc., Arabic would use an actual verb.

Because عود الثقاب is an iḍāfa construction, often translated as the X of the Y.

Here:

• عود = stick
• الثقاب = matches / match
• عود الثقاب = matchstick, literally the stick of the match

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun can make the whole phrase definite

So عود الثقاب is definite because الثقاب is definite.

This pattern is extremely common in Arabic.

Here قرب means near and functions as an adverbial expression of place.

So:

• قرب الشمعة = near the candle
• قرب القابس = near the plug/socket

A useful way to understand it is:

• قرب is followed directly by a noun
• that following noun is in a genitive relationship with it

So the structure is roughly:

• قربَ الشمعةِ
• near the candle

This is why there is no separate word like of or to here.

Yes. Both can express near.

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

The difference is mainly grammatical:

• قرب is used as a noun/adverb-like expression
• قريب is an adjective, usually followed by من

So both are possible, but the structure changes.

In your sentence, قرب gives a compact, natural MSA phrasing.

Because they are definite nouns: the candle, the plug/socket.

Arabic uses الـ to mark definiteness, like the in English.

So:

• شمعة = a candle
• الشمعة = the candle
• قابس = a plug
• القابس = the plug

Since the meaning has already been identified, the sentence uses the definite forms.

Because in Arabic, adjectives normally come after the noun they describe.

So:

• الماس = the short/contact
• الكهربائي = electrical
• الماس الكهربائي = the electrical short/contact

Also, the adjective must agree with the noun in things like:

• definiteness
• gender
• number
• case

That is why both words have الـ:

• الماس
• الكهربائي

If the noun is definite, the adjective must also be definite.

No.

This word is الماس in the expression الماس الكهربائي, which means something like electrical contact or electrical short circuit.

A learner may confuse it with ألماس / الألماس, meaning diamond, but that is a different word.

So in this sentence, الماس الكهربائي is a technical/electrical expression, not anything related to jewelry.

A careful reading would be approximately:

ʿūdu ath-thiqābi qurb ash-shamʿati, wal-māsu al-kahrabāʾiyyu qurb al-qābisi

A few useful pronunciation points:

• ع in عود is the letter ʿayn, which has no exact English equivalent.
• In الثقاب, the ل of الـ is absorbed into ث, so it sounds like ath-thiqāb, not al-thiqāb.
• In الشمعة, the ل is absorbed into ش, so it sounds like ash-shamʿa.
• In القابس, the ل is pronounced normally, so al-qābis.

This happens because ث and ش are sun letters, while ق is a moon letter.

A fully vocalized version could be written as:

عُودُ الثِّقابِ قُرْبَ الشَّمْعَةِ، وَالْماسُ الكَهْرَبائِيُّ قُرْبَ القابِسِ.

The main idea is:

• عُودُ is nominative because it is the topic/subject of the first clause
• الثِّقابِ is genitive because it is the second part of an iḍāfa
• قُرْبَ is in the accusative as an adverbial expression of place
• الشَّمْعَةِ is genitive after قرب
• الْماسُ الكَهْرَبائِيُّ is nominative in the second clause
• القابِسِ is genitive after قرب

In normal unvocalized writing, these endings are usually not shown.

It is basically two parallel nominal clauses joined by و meaning and.

Structure:

• عود الثقاب قرب الشمعة
• والماس الكهربائي قرب القابس

So the sentence is built very symmetrically:

• noun phrase + location
• and
• noun phrase + location

This kind of parallel structure is very common in textbook Arabic because it is clear and easy to read.