Heute wirkt der Sternenhimmel erstaunlich ruhig.

German main clauses follow the verb-second (V2) rule: the finite verb (here wirkt) must be in second position, but the first slot can be almost anything (subject, time, object, etc.).

Putting Heute at the beginning is a common way to emphasize time and sounds very natural in German.

So these are both correct, just with different emphasis:

• Heute wirkt der Sternenhimmel erstaunlich ruhig. (focus on today)
• Der Sternenhimmel wirkt heute erstaunlich ruhig. (neutral; focus more on the sky)

Yes, that version is completely correct.

The difference is mainly information structure / emphasis:

• Heute wirkt der Sternenhimmel … – you highlight today as the topic.
• Der Sternenhimmel wirkt heute … – you highlight the starry sky as the topic.

Grammatically they are the same: the verb wirkt must stay in second position, and both Heute and Der Sternenhimmel can be placed in the first slot.

Wirken has several meanings in German. Two important ones are:

1. to have an effect / to act (e.g. Die Medizin wirkt schnell – The medicine works quickly), and
2. to appear / to seem / to come across as (e.g. Er wirkt müde – He seems tired).

In Heute wirkt der Sternenhimmel erstaunlich ruhig, wirkt has meaning (2):
the starry sky appears / comes across as unusually calm. It does not mean works here.

Der Sternenhimmel is the subject of the sentence, so it is in the nominative case.

• der = nominative singular masculine
• den = accusative singular masculine

The pattern is:

• Nominative (subject): Der Sternenhimmel wirkt ruhig.
• Accusative (object): Ich sehe den Sternenhimmel.

So der is correct here because the sky is doing the “acting” (it is what appears calm).

Sternenhimmel is a compound noun:

• Sterne = stars
• the linking form -n-
• Himmel = sky / heaven

In German compounds, the last part decides the gender and plural.
The last part here is Himmel (masculine), so:

• gender: masculine → der Sternenhimmel
• plural: often die Sternenhimmel (rarely used in practice, but that would be it)

Heute is a temporal adverb (today).

Typical positions:

• At the beginning: Heute wirkt der Sternenhimmel erstaunlich ruhig.
• After the verb / subject: Der Sternenhimmel wirkt heute erstaunlich ruhig.

Both are normal. If there are several adverbials, German tends to prefer the order time – manner – place, but heute itself is flexible.

In erstaunlich ruhig, both words are in the predicative position after a verb (wirkt) and not directly in front of a noun.

In this position, German adjectives:

• keep their basic form (no endings), and
• function a bit like adverbs in English.

Compare:

• ein erstaunlich ruhiger Sternenhimmel → attributive adjectives before a noun, with endings (-er).
• Der Sternenhimmel wirkt erstaunlich ruhig. → predicative, no endings.

So here they behave like predicative adjectives / adverbs and therefore have no extra endings.

There is no comma because erstaunlich is not a second, separate adjective; it functions as an adverbial modifier of ruhig:

• erstaunlich ruhig ≈ astonishingly calm / surprisingly calm

You would use a comma only if they were independent, coordinate adjectives, like:

• ein großer, ruhiger See – a large, calm lake → two separate properties.

Here, erstaunlich just intensifies ruhig, so no comma.

Yes, you can say:

• Heute wirkt der Sternenhimmel erstaunlicherweise ruhig.

Erstaunlicherweise is an adverb that often comments from the speaker’s perspective (interestingly/remarkably, it is calm).
Erstaunlich ruhig sounds more like describing the degree of calmness (very/strikingly calm).

So:

• erstaunlich ruhig → emphasis on how calm it is.
• erstaunlicherweise ruhig → emphasis on your surprise about it being calm.

All three can describe a similar situation, but with nuances:

• ist ruhig – neutral statement of fact: is calm.
• wirkt ruhig – how it comes across / appears to you; more subjective, impression-based.
• scheint ruhig – also seems calm; can sound a bit more tentative or based on limited evidence.

In your sentence:

• Heute wirkt der Sternenhimmel erstaunlich ruhig.
  says: Today, the starry sky comes across as surprisingly calm – focusing on your impression.

Yes, that’s grammatically fine and common:

• Heute wirkt der Sternenhimmel auf mich erstaunlich ruhig.

Wirken auf + Akkusativ highlights on whom something has an effect or impression:

• Er wirkt auf mich sympathisch. – He seems likable to me.

In many cases, auf mich is optional because it’s already clear you’re describing your impression. Leaving it out sounds more neutral and general.

German often uses the present tense to describe:

• current states,
• general impressions,
• things happening right now.

Heute wirkt der Sternenhimmel erstaunlich ruhig focuses on how it is appearing now, today.

If you say:

• Heute hat der Sternenhimmel erstaunlich ruhig gewirkt.
  you shift the focus to the past (e.g. you’re talking about earlier this evening), and it can sound a bit more like a summary of what you perceived over some period.