Ich wundere mich, dass du so früh schon wach bist.

Because sich wundern is normally a reflexive verb in German when it means to be surprised / to wonder.

So the pattern is:

• ich wundere mich
• du wunderst dich
• er/sie wundert sich

A native English speaker often expects a non-reflexive structure, but German uses the reflexive pronoun here as part of the verb.

Because sich wundern takes the accusative reflexive pronoun, not the dative one.

So you get:

• mich
• dich
• sich
• uns
• euch
• sich

Compare:

• Ich wundere mich.
• Du wunderst dich.

This is just something you have to learn with the verb.

The clause dass du so früh schon wach bist gives the content of what is surprising.

So the structure is basically:

• Ich wundere mich = I am surprised / I wonder
• dass du so früh schon wach bist = that you are awake so early already

The whole dass clause works like the thing you are surprised about.

Because in German, a subordinate clause introduced by dass must be separated by a comma.

So:

• Ich wundere mich, dass ...

This comma is not optional in standard German.

Because dass introduces a subordinate clause, and in German subordinate clauses the finite verb normally goes to the end.

Main clause:

• Du bist wach.

Subordinate clause:

• ..., dass du wach bist.

That is one of the most important word-order rules in German.

so früh means so early.

schon here adds the idea of already.

So together, so früh schon means something like:

• so early already
• already awake this early

It emphasizes that the speaker finds the time surprisingly early.

They do different jobs:

• so intensifies früh → so früh = so early
• schon adds the idea of already

So:

• früh = early
• so früh = so early
• früh schon = early already
• so früh schon = so early already

Using both gives a fuller sense of surprise.

wach is an adjective, but here it is used predicatively after sein.

Predicative adjectives in German do not take adjective endings.

Compare:

• Du bist wach.
• ein waches Kind

In ein waches Kind, the adjective comes before a noun, so it gets an ending.
In du bist wach, it comes after sein, so it does not.

Here früh functions adverbially.

It describes the situation of being awake, not a noun. That is why it stays in the basic form:

• du bist früh wach = you are awake early

In so früh, it is part of an adverbial expression meaning so early.

Yes. That is also very natural German.

There is a small difference in feel:

• Ich wundere mich, dass ... = I am surprised that ...
• Es wundert mich, dass ... = It surprises me that ...

Both are correct and common. The second version is a little closer to the English structure It surprises me that ...

Yes, absolutely.

That would mean almost the same thing. The difference is mostly in style:

• Ich wundere mich, dass ... = I find it surprising / I’m surprised
• Ich bin überrascht, dass ... = I’m surprised

Ich bin überrascht can sound a bit more direct and emotional.
Ich wundere mich can sound a bit more like I find it curious/surprising.

Yes, you can.

• Ich wundere mich, dass du so früh schon wach bist.
• Ich wundere mich darüber, dass du so früh schon wach bist.

Both are grammatical.

The version without darüber is very common and natural.
Adding darüber can sound slightly more explicit or a bit more formal, but the meaning stays the same.