بعد ما خلصت الواجب، بعتته لصاحبتي مشان تقراه قبل النوم.

In this sentence, بعد ما means after or once.

So:

• بعد ما خلصت الواجب = after I finished the homework

This is a very common Levantine way to introduce a time clause.
A more formal / MSA-like equivalent would be بعد أن.

It does not mean a literal after what here; it functions as one chunk meaning after.

Because the verb form includes the subject inside it.

• خلص = he finished
• خلصت = I finished / you finished / she finished, depending on context and pronunciation

In normal Arabic spelling, short vowels are usually not written, so خلصت can be ambiguous by itself. Here, since the meaning is already known and the sentence continues naturally from a first-person action, it means I finished.

So Arabic often does not need a separate word for I. The verb already tells you the subject.

That is very normal in Arabic.

الواجب literally means the homework or the assignment, but in many contexts Arabic uses the definite article where English would not.

So:

• خلصت الواجب = I finished the homework / my homework / the homework assignment

The exact English translation depends on context, but the Arabic with الـ is completely natural.

بعتته means I sent it.

It is made of:

• بعت = sent
• -ت = I
• -ه = it / him

So the whole word is:

• بعتته = I sent it

Because الواجب is grammatically masculine, the attached object pronoun is masculine too: -ه.

In Levantine pronunciation, the final -ه is often pronounced more like -o than a clear h.

Because Arabic often attaches object pronouns directly to the verb.

Instead of saying something like:

• I sent it

Arabic says that in one word:

• بعتته

This is very common in Arabic.
Other examples:

• شفته = I saw him / it
• كتبتها = I wrote it (feminine)

So learners often need to get used to whole English phrases being packed into one Arabic word.

لصاحبتي means to my female friend.

It breaks down like this:

• لـ = to
• صاحبة = female friend
• -ي = my

So:

• لصاحبتي = to my female friend

Since صاحبة is feminine, it tells you the friend is female.

Yes, sometimes.

In Levantine, صاحبتي can mean:

• my female friend
• my girlfriend

Context tells you which meaning is intended. In this sentence, it most likely just means my female friend, but both are possible in everyday speech.

Here, مشان means so that, in order to, or for.

So:

• مشان تقراه = so that she can read it

In Levantine, مشان is extremely common. Depending on context, it can mean:

• for
• because of
• in order to / so that

In this sentence, it clearly gives a purpose:

• I sent it to my friend so that she could read it before bed.

Because this is Levantine Arabic, not formal MSA.

In Levantine, the verb قرأ is commonly pronounced and written more like قرا / يقرا in everyday speech.

So:

• MSA: تقرأه
• Levantine: تقراه

Both mean she reads it / she can read it, but the Levantine form is more colloquial and more natural in spoken dialect.

Because the subject is صاحبتي, which is feminine singular.

Here, تقرا means she reads in Levantine.

So:

• صاحبتي ... تقراه = my friend ... reads it

The تـ prefix is used with feminine singular and also with some you forms, so context matters. Here the context makes it clearly she reads it, not you read it.

Because each verb needs its own object if you want to say it explicitly.

The sentence is basically:

• I sent it to my friend
• so that she would read it

English also repeats it here, and Arabic does the same.

So:

• بعتته = I sent it
• تقراه = she reads it

Arabic does not assume that the object automatically carries over to the next verb.

قبل النوم literally means before the sleep, but in natural English it means:

• before sleep
• before going to sleep
• before bed
• at bedtime (depending on context)

This is a very natural Arabic expression.

Also, Arabic often uses الـ in expressions like this where English would not necessarily use the.

Yes, very much so.

The strongest clues are:

• مشان = a very common Levantine word
• تقراه instead of formal تقرأه
• the overall casual spoken-style structure

A speaker of other Arabic dialects would probably understand it, but it sounds specifically Levantine / colloquial rather than formal written Arabic.

Yes, it is completely natural.

The structure is:

• بعد ما خلصت الواجب = after I finished the homework
• بعتته لصاحبتي = I sent it to my friend
• مشان تقراه = so that she could read it
• قبل النوم = before bed

So the sentence flows as:

time clause → main action → purpose clause → time expression

That is a very normal way to build a sentence in Levantine Arabic.