ההודעה שלה הפתיעה אותי, כי לא ציפיתי לתשובה מיד.

Because her message is definite. In Hebrew, possessed nouns are usually definite, so you often get the + noun + possessive, literally the message of hers.

So:

• ההודעה שלה = her message
• הודעה שלה = more like a message of hers

Also, the two ה letters are not a mistake:

• the first ה is the definite article the
• the second ה is part of the noun הודעה

שלה means hers / of her.

It comes after the noun, so Hebrew says:

• ההודעה שלה = literally the message of hers

This is a very common Hebrew pattern. English puts the possessive before the noun (her message), but Hebrew often puts it after.

There is also a shorter, more formal/literary form:

• הודעתה = her message

But in everyday speech, ההודעה שלה is much more natural.

Because the subject, ההודעה (message), is feminine singular.

In the past tense, Hebrew verbs agree with the subject in gender and number:

• הודעה is feminine singular
• so the verb is הפתיעה = surprised (feminine singular)

Compare:

• ההודעה שלה הפתיעה אותי = Her message surprised me
• המסר שלה הפתיע אותי = Her message / her text surprised me if you use מסר, which is masculine

אותי means me.

Hebrew distinguishes between subject and object pronouns, just like English:

• אני = I
• אותי = me

So:

• אני הופתעתי = I was surprised
• היא הפתיעה אותי = She/it surprised me

In your sentence, me is the object of surprised, so Hebrew uses אותי, not אני.

Because אותי already contains the direct-object idea.

With a full noun, Hebrew often uses את before a definite direct object:

• היא הפתיעה את דני = She surprised Danny

But with object pronouns, Hebrew uses special forms:

• אותי = me
• אותך = you
• אותו = him
• אותה = her

So you say:

• הפתיעה אותי

not standardly:

• הפתיעה את אותי

Because the verb לצפות in the sense of to expect normally takes the preposition ל־.

So you learn it as:

• לצפות ל־... = to expect ... / to look forward to ...

Examples:

• ציפיתי לתשובה = I expected a reply
• הם ציפו לשינוי = They expected a change

This is just something to memorize with the verb, like English verbs that need certain prepositions.

Because Hebrew verbs already show the subject.

The ending ־תי in ציפיתי tells you it means I expected.

So:

• ציפיתי = I expected
• לא ציפיתי = I did not expect

Hebrew often leaves out subject pronouns when they are clear from the verb. You can add אני for emphasis or contrast:

• אני לא ציפיתי לתשובה מיד = I wasn’t expecting a reply immediately
  (with extra emphasis on I)

Not always, but in this sentence it clearly means because.

Here it introduces the reason:

• ההודעה שלה הפתיעה אותי, כי...
• Her message surprised me, because...

In some other contexts, especially more formal or older-style Hebrew, כי can also mean something like that or for/since. But for learners, the most common meaning is because, and that is the right meaning here.

מיד means immediately, right away, or at once.

In this sentence:

• לא ציפיתי לתשובה מיד
• I wasn’t expecting a reply right away

Putting מיד at the end is very natural in Hebrew. It tells you the timing of the expected reply.

A closely related alternative would be:

• לתשובה מיידית = an immediate reply

That is similar, but not exactly the same wording.
מיד is an adverb (immediately), while מיידית is an adjective (immediate).

Both are possible, but in this context reply often sounds more natural in English.

Literally, תשובה is answer. But when the topic is a message, English commonly says:

• reply
• response

So:

• לא ציפיתי לתשובה מיד can be understood as
  • I wasn’t expecting an answer immediately
  • I wasn’t expecting a reply right away

All of those fit the Hebrew sentence.

Yes, it is very normal.

The structure is:

• ההודעה שלה = subject
• הפתיעה אותי = verb + object
• כי לא ציפיתי לתשובה מיד = reason clause

So the sentence is basically:

• Her message surprised me, because I wasn’t expecting a reply right away.

That is a very natural Hebrew sentence, both grammatically and stylistically.