الكتاب معار وغرامة التأخير في الرسالة.

In present-tense Arabic, is / am / are is usually not stated.

So:

• الكتاب معار = The book is on loan / checked out
• غرامة التأخير في الرسالة = The late fee is in the message / letter

This is called a nominal sentence: a noun or noun phrase is followed by what is being said about it, without a separate present-tense verb.

معار means lent out, on loan, or in a library context checked out.

It is the passive participle of the verb أعار meaning to lend.

So the idea is not really borrowing from the borrower's point of view, but rather being lent out from the owner's or library's point of view.

For a library book, الكتاب معار is a very natural way to say:

• The book is on loan
• The book is checked out

Because الكتاب is the subject/topic of the first clause.

Arabic often starts a nominal sentence with the thing being talked about, then gives information about it:

• الكتاب = the book
• معار = on loan / lent out

So the structure is basically:

• topic + comment
• the book + on loan

This is very normal in Arabic.

This is an iḍāfa construction, often called a construct phrase.

It is made of:

• غرامة = fee, fine, penalty
• التأخير = delay, lateness

Together, they literally mean:

• the fee of delay
• the fine for lateness

In natural English, that becomes:

• late fee
• overdue fine

So غرامة التأخير is a very common noun phrase type in Arabic: noun + noun, where the second noun explains the first.

Because in an iḍāfa, the first noun usually does not take الـ, but the second noun can.

So:

• غرامة التأخير

is correct because:

• غرامة is the first part of the iḍāfa
• التأخير is the second part

The second noun can be definite, and when it is definite, the whole phrase becomes definite.

So غرامة التأخير means the late fee or the fee for the delay, not just a late fee.

في الرسالة is a prepositional phrase:

• في = in
• الرسالة = the message / letter / notice

In the second clause, it acts as the predicate:

• غرامة التأخير في الرسالة = The late fee is in the message / letter

So this second part is also a complete nominal sentence:

• subject: غرامة التأخير
• predicate: في الرسالة

Yes.

The sentence has two parts joined by و meaning and:

1. الكتاب معار
2. غرامة التأخير في الرسالة

So the structure is:

• The book is on loan, and the late fee is in the message/letter.

Arabic very often joins short nominal clauses with و in this simple way.

No. الرسالة can mean several things depending on context, including:

• letter
• message
• email
• notice

So in a modern context, في الرسالة could mean:

• in the message
• in the email
• in the notice

The exact English translation depends on where the sentence comes from.

In fully vocalized formal Arabic, it would be:

الكتابُ مُعارٌ وغرامةُ التأخيرِ في الرسالةِ

Here is why:

• الكتابُ — nominative, because it is the subject of the first clause
• مُعارٌ — nominative, because it is the predicate of the first clause
• غرامةُ — nominative, because it is the subject of the second clause
• التأخيرِ — genitive, because it is the second noun in the iḍāfa
• الرسالةِ — genitive, because it comes after في

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

Because ر is a sun letter.

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

So:

• الرسالة is pronounced ar-risāla
• not al-risāla

The same thing happens in التأخير:

• it is pronounced at-taʾkhīr
• not al-taʾkhīr

This is a pronunciation rule only; the spelling still uses الـ.