بعد الاستراحة أعود إلى المكتب وأكتب رسالة إلى الموظفة في البنك.

Because بعد الاستراحة is a time expression meaning after the break. Arabic very often puts time expressions at the beginning of the sentence to set the scene first.

So the structure is roughly:

• بعد الاستراحة = after the break
• أعود = I return
• إلى المكتب = to the office
• وأكتب رسالة = and write a letter

You could move the time phrase later, but the original order is very natural in MSA.

بعد functions like a preposition-like word or adverbial noun meaning after.

In بعد الاستراحة:

• بعد = after
• الاستراحة = the break

The noun after بعد is treated as dependent on it, so in fully vowelled Arabic it appears in the genitive:

• بعدَ الاستراحةِ

So yes, for a learner, it is easiest to think of بعد as a word that means after and is followed by a noun.

Because the sentence refers to a specific, known break: the break.

Arabic uses الـ to mark definiteness, just like English uses the. So:

• استراحة = a break
• الاستراحة = the break

If you said بعد استراحة, that would mean after a break or after some break, which is less specific.

It is built into the verbs أعود and أكتب.

In the imperfect tense, the prefix أ- often marks I:

• أعود = I return
• أكتب = I write

So Arabic does not need a separate subject pronoun here. You could add أنا for emphasis:

• أنا أعود إلى المكتب...

But normally it is unnecessary.

They are in the imperfect form, which often corresponds to the present tense in English, but it can also express:

• present actions
• habitual actions
• near-future actions, depending on context

So here the sentence could mean something like:

• After the break, I return to the office and write a letter
• or, in a routine sense, After the break, I usually return to the office and write a letter

Context tells you which is meant.

Because two different parts of the sentence need to in Arabic.

1. أعود إلى المكتب

   • عاد إلى means to return to
   • so إلى marks the destination

2. رسالة إلى الموظفة

   • رسالة إلى... means a letter to...
   • so إلى marks the recipient

Even though English also uses to in both places, the grammar is different:

• with the verb return
• with the noun letter

Because المكتب is definite, while رسالة is indefinite.

• المكتب = the office
• رسالة = a letter

This suggests:

• the office is a specific office already known from context
• the letter is not a specific previously mentioned letter

If you wanted the letter, you would say الرسالة.

Because الموظفة is feminine and means the female employee.

Compare:

• الموظف = the male employee
• الموظفة = the female employee

Arabic usually marks natural gender clearly in singular nouns for people. So if the employee is a woman, الموظفة is the correct form.

Most naturally, it describes الموظفة:

• الموظفة في البنك = the employee at/in the bank

So the meaning is most likely:

• I return to the office and write a letter to the female employee at the bank

In other words, في البنك is most naturally attached to الموظفة, not to أكتب.

If you wanted to make it clearer that the writing happens at the bank, you would usually rewrite the sentence more explicitly.

Because في means in or at, while إلى means to.

Here, في البنك describes location:

• في البنك = in the bank / at the bank

If you said إلى البنك, that would suggest movement toward the bank:

• to the bank

So:

• الموظفة في البنك = the employee at the bank
• الموظفة إلى البنك would not fit this meaning

و simply means and.

So:

• أعود إلى المكتب وأكتب رسالة = I return to the office and write a letter

In context, the actions are understood as happening in sequence, especially because the sentence begins with بعد الاستراحة. But و itself does not strongly emphasize then.

If you wanted a clearer then/after that, Arabic could use:

• ثم = then

For example:

• بعد الاستراحة أعود إلى المكتب ثم أكتب رسالة

That makes the sequence more explicit.

Arabic word order is more flexible than English word order.

This sentence begins with a time phrase, then uses verbs:

• بعد الاستراحة = time first
• أعود = verb
• وأكتب = second verb

That is completely natural in Arabic. English often prefers:

• After the break, I return to the office and write a letter

So the overall structure is similar in meaning, but Arabic does not need to state the subject separately, and it often likes to place time information early.

In fully vowelled, formal MSA, the sentence would be:

بَعْدَ الاستراحةِ أعودُ إلى المكتبِ وأكتبُ رسالةً إلى الموظفةِ في البنكِ

Here is why:

• بعدَ: accusative as an adverbial expression of time
• الاستراحةِ: genitive after بعد
• أعودُ: indicative verb
• إلى المكتبِ: genitive after إلى
• أكتبُ: indicative verb
• رسالةً: accusative direct object
• إلى الموظفةِ: genitive after إلى
• في البنكِ: genitive after في

In normal unvowelled writing, these endings are usually not written, but they are still part of the formal grammar.