في كل أسبوع أذهب إلى المكتبة مرة أو مرتين.

Yes. كل أسبوع is very common and often the more natural way to say every week.

The version in your sentence, في كل أسبوع, is also understandable and means something like in every week / every week. Learners often notice the في because English does not always use a preposition here.

A simple way to think about it:

• كل أسبوع = every week
• في كل أسبوع = literally in every week

In many contexts, both work, but كل أسبوع is often shorter and more idiomatic.

After كل, Arabic usually uses a singular noun to mean every ....

So:

• كل يوم = every day
• كل أسبوع = every week
• كل شهر = every month

This is different from English, where learners may expect something like every weeks, but English also uses the singular after every. Arabic works similarly here.

أذهب means I go.

The verb itself already tells you the subject is I, because the prefix أـ marks first person singular in the present tense.

So:

• أذهب = I go
• تذهب = you go / she goes
• يذهب = he goes
• نذهب = we go

That is why Arabic does not need a separate subject pronoun here. You could say أنا أذهب, but أنا is optional unless you want extra emphasis.

Because Arabic verbs usually include the subject inside the verb form.

In أذهب, the أـ already means I. So the sentence does not need أنا.

Compare:

• أذهب إلى المكتبة = I go to the library
• أنا أذهب إلى المكتبة = I go to the library / I go to the library

The second version adds emphasis or clarity, but the first is completely normal.

Because ذهب إلى is the standard way to say go to a place.

So:

• أذهب إلى المكتبة = I go to the library
• أذهب إلى المدرسة = I go to the school
• أذهب إلى البيت = I go home / to the house

English uses to, and Arabic usually uses إلى in the same kind of idea.

المكتبة means the library, while مكتبة means a library.

So the sentence is talking about a specific type of place, understood as the library:

• إلى المكتبة = to the library
• إلى مكتبة = to a library

In many real contexts, either can be possible depending on meaning, but your sentence uses the definite form المكتبة.

This phrase expresses frequency: once or twice.

Breakdown:

• مرة = one time / once
• مرتين = two times / twice
• أو = or

So:

• مرة أو مرتين = once or twice

In this sentence, it tells you how often the action happens within each week.

Because Arabic handles one time and two times differently.

1. مرة

This is the ordinary singular noun meaning a time / one occasion.

2. مرتين

This is the dual form, meaning two times.

Arabic has a special grammatical form for exactly two things, called the dual. English does not have this.

So:

• مرة = one time
• مرتان = two times (nominative)
• مرتين = two times (accusative/genitive)

In your sentence, مرتين is the correct form.

Because the dual in Arabic changes form depending on grammatical case.

For dual nouns:

• ـان = nominative
• ـين = accusative or genitive

In this sentence, مرتين is used in an adverbial sense of frequency, so it appears in the accusative form.

That is why you get:

• مرة أو مرتين

not

• مرة أو مرتان

This is a common point for learners because English has no case endings like this.

In fully vowelled Arabic, yes, it would normally be written مرةً.

But in normal everyday Arabic writing, short vowels and tanwīn are usually not written, so you usually just see:

• مرة أو مرتين

If fully vocalized, it could appear as:

• مَرَّةً أَوْ مَرَّتَيْنِ

So the case ending is there grammatically, even if it is not usually shown in ordinary text.

Yes, Arabic word order is fairly flexible, and that sentence is still understandable.

Your original sentence:

• في كل أسبوع أذهب إلى المكتبة مرة أو مرتين

puts the time expression first, which gives it a bit of emphasis: As for every week, I go to the library once or twice.

A different order like:

• أذهب إلى المكتبة مرة أو مرتين في كل أسبوع

is also possible and still natural.

Arabic often moves time phrases around more freely than English does.

Yes, أو means or, and here it suggests approximation or variation.

So مرة أو مرتين means:

• sometimes once
• sometimes twice
• roughly once or twice

It does not necessarily mean the speaker is confused. It often simply gives an approximate frequency.

Yes. In Modern Standard Arabic, أذهب is the standard and correct choice.

But in many spoken dialects, people often use other verbs, such as forms related to روح instead of ذهب.

For example, in speech you may hear dialect forms meaning I go, but for MSA study, أذهب إلى المكتبة is exactly what you should learn.

So:

• أذهب = standard written/formal Arabic
• other forms may appear in dialects

If you want a more grammar-focused view, the nouns are behaving like this:

• في كل أسبوع
  After في, the noun is in the genitive. So أسبوع is genitive here.

• إلى المكتبة
  After إلى, المكتبة is also genitive.

• مرة أو مرتين
  This frequency expression is in the accusative, which is why the dual appears as مرتين.

So in fully vocalized MSA, you could think of it roughly as:

• في كلِّ أسبوعٍ
• أذهبُ إلى المكتبةِ
• مرةً أو مرتينِ

This is a more advanced detail, but it helps explain why the endings are what they are.