Tôi đã viết lý do đổi trả trong email.

Đã is a past/completed-action marker.

So:

• Tôi viết = I write / I am writing / I wrote (depends on context)
• Tôi đã viết = I wrote / I have written

Vietnamese verbs do not change form the way English verbs do, so words like đã help show time.

In Vietnamese, verbs do not conjugate for tense.

The verb stays viết whether the action is present, past, or future. Time is usually shown by:

• time words: hôm qua = yesterday, ngày mai = tomorrow
• markers: đã (past/completed), đang (in progress), sẽ (future)
• context

So viết always stays viết.

The word order is:

• Tôi = I
• đã viết = wrote / have written
• lý do đổi trả = the reason for the exchange/return
• trong email = in the email

So Vietnamese is following a normal Subject + Verb + Object + Location/Context pattern here.

Lý do means reason.

Đổi trả refers to exchanging or returning something, usually a product. It is a common customer-service/shopping phrase.

So lý do đổi trả means:

• reason for exchange/return
• reason for returning the item
• depending on context, reason for a refund or replacement request

It is a fixed retail/customer-service expression made from:

• đổi = exchange
• trả = return

Together, đổi trả often works like one combined idea: exchange/return.

In shopping contexts, Vietnamese often groups them together because stores commonly talk about đổi trả hàng = exchanging or returning goods.

Here trong email most naturally means in the email, meaning the reason was written inside the email's content.

That is different from:

• qua email = by email / via email
• bằng email = by email (less common in everyday speech than qua email)

So:

• Tôi đã viết lý do đổi trả trong email = I wrote the return/exchange reason in the email
• Tôi đã gửi lý do đổi trả qua email = I sent the return/exchange reason by email

Because email is very commonly used in modern Vietnamese, especially in everyday speech and business communication.

You may also see:

• thư điện tử = a more formal or more purely Vietnamese term
• email = much more common in normal use

So trong email sounds natural.

Yes, it can be omitted if the time is already clear from context.

For example:

• Tôi viết lý do đổi trả trong email rồi.
• Hôm qua tôi viết lý do đổi trả trong email.

Vietnamese often leaves tense markers out when the listener can understand the time from context.

But with no other time clue, đã is helpful because it clearly shows the action is completed.

No. Tôi is just the neutral, safe, standard way to say I.

Depending on who is speaking and to whom, Vietnamese might use:

• mình
• em
• anh
• chị
• con
• cháu

But tôi is a good general-purpose pronoun, especially in writing, formal situations, or when you want to sound polite and neutral.

Yes, it is understandable and natural.

It sounds like a clear written statement, especially in a customer-service or email context.

Depending on the situation, a native speaker might also say:

• Tôi đã viết lý do đổi trả trong email rồi.
  Adds rồi, which emphasizes that it has already been done.

• Tôi đã nêu lý do đổi trả trong email.
  Nêu sounds a bit more formal, like stated/mentioned.

• Tôi đã ghi lý do đổi trả trong email.
  Ghi can sound like wrote down/noted.

But your original sentence is fine.

Vietnamese does not use articles like a, an, and the the way English does.

So Vietnamese often just says:

• lý do = reason / the reason
• email = an email / the email

Which one is meant depends on context.

In this sentence, English might naturally translate it as the reason and the email, but Vietnamese does not need separate article words for that.