استلفت كتاب من زميلتي، ووعدتها ارجعه بكرا.

It is Levantine colloquial Arabic.

A few clues:

• بكرا is the everyday Levantine word for tomorrow
• there are no case endings
• the structure is more conversational than formal written Arabic

A more MSA-like version would be:

استعرتُ كتابًا من زميلتي، ووعدتُها أن أُعيده غدًا.

So the sentence you have is natural for spoken Levantine, not formal Standard Arabic.

In Levantine, استلف commonly means to borrow.

So:

• استلفت كتاب = I borrowed a book

A related verb is:

• سلّف = to lend

So:

• سلّفني كتاب = he/she lent me a book

This is one place where dialect and MSA differ a bit, because in MSA learners often meet استعار for borrow.

Because the verb already shows the subject.

In استلفت and وعدت:

• the ending -ت tells you the subject is I

So:

• استلفت = I borrowed
• وعدت = I promised

Arabic often leaves out subject pronouns when the verb already makes them clear.

Arabic does not have a separate word for a/an.

So:

• كتاب = a book or just book in an indefinite sense
• الكتاب = the book

Here, because there is no الـ, كتاب is understood as a book.

زميلتي means my female classmate / my female colleague, depending on context.

Breakdown:

• زميلة = a female classmate or colleague
• -ي / -يـ = my

When a feminine noun ends in ـة, that t sound reappears before a suffix:

• زميلة
  • ي → زميلتي

So it is not just vocabulary; it also shows possession:

• زميلتي = my female classmate/colleague

If it were masculine, you would get:

• زميلي = my male classmate/colleague

Because Arabic, like English, uses from with borrow.

So:

• استلفت كتاب من زميلتي = I borrowed a book from my classmate

Here من marks the source: the person you got the book from.

Because two different things come together:

• the first و = and
• وعدتها = I promised her

So:

• و + وعدتها → ووعدتها

This is completely normal in Arabic spelling. It is not a typo.

Also, وعدتها breaks down as:

• وعدت = I promised
• ها = her

So وعدتها means I promised her.

In colloquial Levantine, أن is often omitted.

In MSA, you would more likely say:

• وعدتها أن أعيده

But in everyday Levantine, it is very normal to say:

• وعدتها ارجعه بكرا

So the meaning is still I promised her that I’d return it tomorrow, even without أن.

Because after verbs like want, have to, promise, and similar expressions, Levantine often uses the bare imperfect rather than the regular b- present form.

Compare:

• برجع/برجّع = ordinary present or habitual sense, depending on the verb and context
• ارجعه here = return it / that I return it / that I’ll return it

So in:

• وعدتها ارجعه بكرا

the idea is not a simple present like I return it, but a complement after promised: promised to return it.

This is very similar to other Levantine patterns such as:

• بدي روح = I want to go
• لازم ادرس = I have to study

It refers back to كتاب.

So:

• ارجع/رجّع = return
• -ه = it / him

Since كتاب is grammatically masculine, the attached object pronoun is -ه.

So ارجعه means return it, with it = the book.

Because بكرا is the normal Levantine everyday word for tomorrow.

In MSA, you usually learn:

• غدًا

In Levantine, you will much more often hear:

• بكرا or بكرة

So this is a good example of a very common dialect vocabulary difference.

Yes. That would also be natural.

Adding رح or حـ makes the future more explicit:

• وعدتها رح ارجعه بكرا = I promised her I’d return it tomorrow

Without رح, the sentence is still clear because:

• the verb comes after promised
• بكرا already points to the future

So both are possible; the version without رح is simply a bit lighter and very natural in speech.