بعد دقيقة وصلت رسالة عالتلفون.

In this sentence, بعد دقيقة means a minute later / after a minute.

Because the verb is in the past (وصلت), the whole sentence is describing something that happened, so the natural meaning is:

• A minute later, a message arrived on the phone.

In other contexts, بعد دقيقة can also mean in a minute, especially when talking about the future. Context tells you which meaning is intended.

Because it means a minute, not the minute.

• بعد دقيقة = after a minute
• بعد الدقيقة = after the minute or after that specific minute

Also, in colloquial Levantine, you normally do not write or say the formal case endings, so you just see دقيقة.

Because the subject is رسالة, and رسالة is a feminine noun in Arabic.

So:

• وصلت رسالة = a message arrived

The verb agrees with رسالة in gender, so it takes the feminine form.

A useful comparison:

• وصل كتاب = a book arrived
• وصلت رسالة = a message arrived

By itself, رسالة just means message.

In this phone context, many speakers will understand it as something like:

• a text message
• a message notification
• a message received on the phone

If you want to be more specific, you might hear:

• رسالة نصية = text message
• مسج = message/text (very common colloquial borrowing from English)

So رسالة is general, but the context makes it sound like a phone message.

عالتلفون is a colloquial contraction of على التلفون.

So:

• على
  • التلفون → عالتلفون

Here it means something like:

• on the phone
• to the phone
• on the mobile

In natural English, the whole idea is simply that the message arrived on the phone.

It is commonly pronounced roughly like ʿat-telefon.

That happens because التلفون starts with ت, and ت is a sun letter. In Arabic, the ل of الـ is absorbed into the following sun letter in pronunciation.

So:

• written: على التلفون
• spoken more like: ʿa t-telefon
• contracted in writing: عالتلفون

So even though you still see the ل in writing, you usually do not hear it clearly in speech.

Because التلفون is much more natural in everyday Levantine speech.

• التلفون = everyday colloquial phone/telephone
• الهاتف = more formal / more MSA-like

A native speaker in conversation is much more likely to say تلفون or موبايل than هاتف.

Yes, you can change the order, but the meaning and emphasis shift a little.

The sentence as written:

• بعد دقيقة وصلت رسالة عالتلفون

is a very natural storytelling order in Arabic: time expression + verb + subject

It feels like:

• A minute later, a message arrived on the phone.

If you say:

• بعد دقيقة الرسالة وصلت عالتلفون

that is also possible, but it gives more emphasis to the message. It sounds a bit more marked or specific.

So the original order is very normal and natural.

Yes, absolutely. That would also sound natural in Levantine.

Both are common:

• وصلت رسالة = a message arrived / reached
• إجت رسالة = a message came

The difference is small. In many everyday situations, they are almost interchangeable.

• وصلت can feel slightly more like arrived/reached
• إجت can feel slightly more like came

But both are very normal.

This is a very useful distinction.

• عالتلفون usually means on the phone or onto the phone
  
  • something appeared, arrived, or showed up on the phone
• بالتلفون usually means by phone / over the phone

So:

• وصلت رسالة عالتلفون = a message arrived on the phone
• حكينا بالتلفون = we talked on the phone / by phone

So in your sentence, عالتلفون is the natural choice because the message is appearing on the phone, not being done by means of the phone.