صاحبتي عايزة غدا بعد الشغل.

A reasonable pronunciation is:

ṣāḥbti ʿāyza ġada baʿd eš-šoġl

A rough English-style guide could be:

SAAH-bti AAY-za GHA-da baʕd esh-SHOGHL

A few sounds to notice:

• ح in صاحبتي is a strong, breathy h
• ع in عايزة and بعد is a throat sound with no exact English equivalent
• غ in غدا is like a French or Parisian r
• الشغل is pronounced eš-šoġl, not al-shoghl, because ال changes sound before ش

Different speakers may pronounce some vowels a little differently, but this is a good target.

صاحبتي means my female friend.

It breaks down like this:

• صاحبة = a female friend / female companion
• -ي = my

So:

• صاحبتي = my female friend

Very important: this tells you the friend is female, not the speaker. A man or a woman can both say صاحبتي.

Yes. In everyday Egyptian Arabic, صاحبتي can mean either:

• my female friend
• my girlfriend

Context decides which one is meant.

If the situation is romantic, people will often understand it as girlfriend. If the context is casual or social, it may just mean female friend.

So this word can be a little ambiguous, just like some relationship words in English can be.

Because صاحبتي is feminine, and عايز changes for gender.

• عايز = masculine
• عايزة = feminine

So:

• صاحبي عايز = my male friend wants
• صاحبتي عايزة = my female friend wants

This is very common in Egyptian Arabic: adjectives and participle-like words often agree with the gender of the person they describe.

Not exactly in the same way as the English verb want.

In Egyptian Arabic, عايز / عايزة is originally an active participle, but in everyday speech it functions very much like want.

So:

• أنا عايز = I want
• هي عايزة = she wants
• إحنا عايزين = we want

This is the normal colloquial way to say want.

A related thing learners often notice: there is no separate word for is here. In present-tense Arabic sentences like this, you normally do not say a word for is/am/are.

Here it means lunch.

In Egyptian Arabic:

• غدا = lunch

For tomorrow, Egyptian Arabic usually says:

• بكرة = tomorrow

You may know that in Modern Standard Arabic, غدًا can mean tomorrow, but in everyday Egyptian speech بكرة is much more common for that meaning.

So in this sentence, غدا is understood as lunch.

Because in Egyptian Arabic, it is completely natural to say want + noun.

So:

• عايزة غدا = she wants lunch

You do not need to add a verb like eat if the meaning is clear.

If you want to be more explicit, you could say:

• صاحبتي عايزة تتغدى بعد الشغل

That means something like My friend wants to have lunch after work.

So both patterns are possible:

• عايزة غدا = wants lunch
• عايزة تتغدى = wants to have lunch

It means after work.

Breakdown:

• بعد = after
• الشغل = the work / work / the job

So literally it is something like after the work, but in natural English we usually say after work.

In Egyptian Arabic, الشغل is a very common word for:

• work
• job
• employment
• workplace activity

Depending on context, بعد الشغل can mean:

• after work
• after the job
• after finishing work

Because Arabic and English do not use definiteness in exactly the same way.

In Arabic, it is very normal to say:

• بعد الشغل = after work
• في البيت = at home
• في المدرسة = at school

Even when English would not use the, Arabic often does.

Also, in pronunciation, ال changes here because ش is a sun letter:

• written: الشغل
• pronounced: eš-šoġl

So the l sound of ال is not heard.

Yes, it is natural and understandable.

A very everyday Egyptian sentence could be exactly this:

• صاحبتي عايزة غدا بعد الشغل

But you may also hear small variations, such as:

• صاحبتي عايزة تتغدى بعد الشغل
  more explicitly: My friend wants to have lunch after work

• بعد الشغل صاحبتي عايزة غدا
  same meaning, but with after work moved to the front for emphasis

• صاحبتي عايزة غدا بعد ما تخلص الشغل
  more literally: My friend wants lunch after she finishes work

So your original sentence is good, and there are also several natural alternatives depending on style and emphasis.