القابس قرب شاحن الهاتف.

Because this is a present-tense nominal sentence in Arabic. In Modern Standard Arabic, the verb to be is usually not stated in the present tense.

So:

• القابس قرب شاحن الهاتف = The plug is near the phone charger

But in the past or future, Arabic would use a verb such as كان.

Here قرب means near or close to.

In grammar terms, it is often treated as a noun of place / adverbial expression used like near in English. So the phrase:

• قرب شاحن الهاتف
  means
• near the phone charger

A very similar alternative is:

• بالقرب من شاحن الهاتف
• قريب من شاحن الهاتف

All of these can express the idea of being near something.

Because القابس is definite here: it means the plug, not just a plug.

The prefix الـ is the Arabic definite article, equivalent to the in English.

So:

• قابس = a plug / plug
• القابس = the plug

Because شاحن الهاتف is an iḍāfa construction, often called a genitive construct or possessive construction.

In an iḍāfa:

1. The first noun does not take الـ
2. The second noun can be definite or indefinite
3. The whole phrase gets its definiteness from the second noun

So:

• شاحن الهاتف literally = charger of the phone
• natural English = the phone charger

You do not say الشاحن الهاتف for this meaning.

Because in an iḍāfa, the whole phrase becomes definite if the second noun is definite.

Here:

• الهاتف = the phone
• therefore شاحن الهاتف = the phone charger

So even though شاحن itself has no الـ, the full phrase is still definite.

Because شاحن is the first word in an iḍāfa.

In Arabic, the first noun in an iḍāfa:

• does not take الـ
• does not take tanwīn

So this is correct:

• شاحن الهاتف

Not:

• شاحنٌ الهاتف
• الشاحن الهاتف

for this particular structure.

It would typically be:

• القابِسُ قُرْبَ شاحِنِ الهاتِفِ

Here is why:

• القابِسُ: nominative, because it is the subject/topic
• قُرْبَ: accusative as an adverbial expression
• شاحِنِ: genitive, because it follows قرب in this construction
• الهاتِفِ: genitive, because it is the second term of the iḍāfa

In normal everyday writing, these short vowels are usually omitted.

Yes. That is also correct and very natural.

Compare:

• القابس قرب شاحن الهاتف
• القابس قريب من شاحن الهاتف

Both mean roughly The plug is near the phone charger.

The difference is mainly structural:

• قرب = near as an adverbial/location expression
• قريب من = close to using the adjective قريب

Both are common and useful.

Yes. In Modern Standard Arabic, قابس is a standard word for an electrical plug.

However, in everyday spoken dialects, many speakers often use other words, depending on the country. For example, some people say فيشة in casual speech.

So for MSA, القابس is a good word to learn.