بعد اسبوع عندي امتحان، ولازم ادرس.

A common approximate pronunciation is:

baʿd usbuuʿ ʿandii imtiḥaan, w-laazem adros

A few notes:

• بعد = baʿd
• اسبوع = usbuuʿ or isbuuʿ depending on speaker
• عندي = ʿandii
• امتحان = imtiḥaan
• ولازم = w-laazem
• ادرس = adros in a simple transliteration

Pronunciation varies a bit across Levantine dialects, but this will be understood.

Yes, بعد literally means after, but in this kind of sentence بعد اسبوع is commonly understood as:

• after a week
• in a week
• a week from now

So in natural English, بعد اسبوع عندي امتحان is usually best understood as I have an exam in a week.

Because the time expression بعد اسبوع already makes the sentence future.

Arabic, like English, does not always need an explicit future marker if the time is clear. Compare:

• In a week I have an exam.
• بعد اسبوع عندي امتحان.

Both sound natural because the time phrase already tells you it is about the future.

You could also say:

• بعد اسبوع رح يكون عندي امتحان

That is more explicitly future, but the original sentence is perfectly normal.

This is a very common Arabic structure.

• عند literally means something like at
• عندي literally means at me

So عندي امتحان is literally something like at me, an exam, but the natural English meaning is:

• I have an exam

Arabic often uses this kind of structure instead of a separate verb meaning to have.

Yes. Both are natural.

• بعد اسبوع عندي امتحان
• عندي امتحان بعد اسبوع

The difference is mostly about emphasis:

• بعد اسبوع... puts the time first: In a week...
• عندي امتحان... puts the fact first: I have an exam...

Both are good Levantine-style sentences.

لازم means necessary, and in everyday speech it works like:

• must
• have to
• need to

So:

• لازم ادرس = I have to study / I need to study

It is one of the most common ways to express obligation in Levantine Arabic.

This is a very important pattern in Levantine.

In many Levantine dialects:

• بدرس = I study / I am studying / I usually study
• ادرس = the bare imperfect form, often used after words like لازم, بدي, ممكن, etc.

So:

• بدرس by itself is a normal present/habitual form
• لازم ادرس is the correct pattern after لازم

That is why لازم بدرس sounds wrong or at least nonstandard in this context.

Because this is informal dialect writing.

In casual Levantine Arabic writing, especially in texting or everyday typed Arabic, people often leave out the hamza spelling:

• أسبوع → اسبوع
• أدرس → ادرس

This does not usually change the meaning. It is just a looser, more colloquial writing style.

If you were writing more formally, you would often see:

• بعد أسبوع عندي امتحان، ولازم أدرس.

It is really:

• و = and
• لازم = must / have to / necessary

But in Arabic script, short words like و attach directly to the next word, so it is written:

• ولازم

So you can think of it as w + laazem.

Usually عندي امتحان is the more natural choice here.

• عندي is the normal way to say I have
• معي literally means with me

معي is often used for things you physically have with you, like:

• معي مصاري = I have money on me
• معي المفتاح = I have the key with me

For scheduled events or general possession, عندي is usually better:

• عندي امتحان = I have an exam

Because the sentence means an exam, not the exam.

• امتحان = an exam
• الامتحان = the exam

So:

• عندي امتحان = I have an exam
• عندي الامتحان would mean something more like I have the exam, which is a different idea and usually less natural here unless a specific exam has already been mentioned.

Also, in colloquial Arabic, indefinite nouns are often just left bare, with no extra ending.

Yes. Depending on the country and speaker, you may also hear:

• لازم ادرس
• لازم اذاكر

Both can mean I have to study, though ذاكر / يذاكر is more common in some regions than others.

So the original sentence is very natural, but there are regional alternatives.