بعد ما الطرد اتاخر، خدمة العملاء اكدت ميعاد التوصيل المتوقع.

In Egyptian Arabic, بعد ما is a very common way to mean after when it is followed by a whole clause:

• بعد ما الطرد اتأخر = after the package got delayed

If you use بعد by itself, it more naturally goes before a noun phrase:

• بعد التأخير = after the delay

So here, because الطرد اتاخر is a full clause, بعد ما is the natural choice.

Not exactly. اتاخر / اتأخر in Egyptian Arabic means to be late or to get delayed.

So Arabic is expressing the idea more like:

• the package got delayed
• the package was late

English often uses a passive here: was delayed.
Arabic does not need a passive form in this sentence; اتاخر already gives the right meaning naturally.

Because Arabic usually does not need a separate verb like was in this kind of sentence.

English says:

• the package was delayed

Egyptian Arabic says more literally:

• the package got delayed / became late

So اتاخر carries the whole idea by itself. You do not need an extra helping verb.

Because it is in the past tense, third person masculine singular, which is the basic form of the verb.

The subject is الطرد (the package), and طرد is grammatically masculine singular, so the verb appears in its plain past form:

• اتاخر = it got delayed

If the subject changed, the verb would change too. For example:

• الشحنة اتأخرت = the shipment got delayed
  because شحنة is feminine, so the verb ends in -ت

Because the subject is خدمة العملاء, and the head word there is خدمة, which is feminine singular.

So the verb agrees with خدمة, not with العملاء:

• خدمة العملاء اكدت = customer service confirmed

The ending -ت marks she/it in the past tense for a feminine singular subject.

So even though العملاء means customers and is plural, the whole phrase is headed by خدمة.

This is an idafa construction, also called a genitive or possessive construction:

• خدمة = service
• العملاء = the customers

Together:

• خدمة العملاء = customer service
  literally service of the customers

A few useful points:

• The first noun usually does not take ال
• The second noun can make the whole phrase definite
• The first noun is the grammatical head, so it controls agreement

That is why the verb agrees with خدمة.

In Egyptian Arabic, ميعاد is very common and means something like:

• appointment
• scheduled time
• date/time
• timing

In delivery contexts, ميعاد التوصيل means:

• delivery time
• delivery date
• delivery appointment/window

موعد can also mean something similar, but ميعاد is especially common in everyday Egyptian speech.

It describes the whole idea of the delivery time/date:

• ميعاد التوصيل المتوقع = the expected delivery date/time

Word-for-word, it looks like:

• ميعاد = موعد / scheduled time
• التوصيل = delivery
• المتوقع = expected

So the phrase means the expected delivery موعد.

A learner may notice that المتوقع could seem to attach to either ميعاد or التوصيل, because both are masculine singular. In practice, the meaning is understood from context as the expected delivery time/date.

You could say لما الطرد اتأخر, but it would mean when the package got delayed, not specifically after the package got delayed.

So the difference is:

• بعد ما = after
• لما = when

In this sentence, بعد ما is better because it clearly shows sequence: first the package was delayed, then customer service confirmed the delivery time.

A natural pronunciation would be roughly:

baʿd ma eṭ-ṭard itʾakhkhar, khidmit il-ʿomala akkadet miʿaad it-tawṣeel il-mutawaqqaʿ

A few pronunciation notes:

• الطرد is pronounced eṭ-ṭard because ال assimilates before ط
• خدمة often sounds like khidmit in this construction, not pause-form khidma
• التوصيل is pronounced it-tawṣeel
• أكدت is commonly pronounced akkadet

That is mostly a spelling issue.

In less formal writing, people often leave out the hamza and write:

• اتاخر

A more careful spelling is:

• اتأخر

Both represent the same word in everyday Egyptian Arabic. Informal Arabic writing often simplifies hamza spelling, especially in chat, texting, and social media.

Yes, the word order can change.

The original sentence begins with the time clause for emphasis:

• بعد ما الطرد اتاخر، خدمة العملاء اكدت ميعاد التوصيل المتوقع.

You could also say:

• خدمة العملاء اكدت ميعاد التوصيل المتوقع بعد ما الطرد اتاخر.

Both are natural. The version with بعد ما... first sets up the situation before giving the main action, which is very common in both Arabic and English.