Mein Zuhause ist ruhig.

Because Zuhause is grammatically neuter: das Zuhause.
In the nominative singular, the possessive form for a neuter noun is mein.

So:

• mein Zuhause
• mein Haus
• mein Zimmer

Compare:

• meine Wohnung because Wohnung is feminine
• mein Garten because Garten is masculine

Zuhause usually means home in the sense of the place where you feel at home or where you live. It is often more personal and emotional than Haus.

• Haus = house, the building itself
• Zuhause = home

So Mein Zuhause ist ruhig sounds more like talking about your home environment, not just the physical building.

Because it is being used here as a noun, and all nouns in German are capitalized.

In Mein Zuhause ist ruhig, Zuhause is a noun meaning home.

Be careful, because German also has zu Hause, written as two words, which is usually an adverbial expression meaning at home.

Compare:

• Mein Zuhause ist ruhig. = My home is quiet.
• Ich bin zu Hause. = I am at home.

This is a very common question.

• das Zuhause = a noun meaning home
• zu Hause = an adverbial phrase meaning at home

Examples:

• Mein Zuhause ist klein.
• Ich arbeite zu Hause.

So in your sentence, Zuhause is the subject of the sentence, which is why it is a noun.

Ist is the 3rd person singular form of the verb sein (to be).

The subject is Mein Zuhause, which is grammatically it:

• mein Zuhause → it
• therefore: ist

A quick comparison:

• ich bin
• du bist
• er/sie/es ist

So Mein Zuhause ist ruhig follows the same pattern as:

• Das Haus ist groß.
• Der Raum ist hell.

Because German main clauses normally follow the verb-second rule.

In a basic statement, the conjugated verb usually comes second:

• Mein Zuhause | ist | ruhig

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

You could also move another element to the front, and the verb would still stay second:

• Heute ist mein Zuhause ruhig.

So the key rule is not subject first; it is usually conjugated verb in second position.

Because ruhig is not being used before a noun here. It is a predicate adjective, coming after the verb sein.

In German, predicate adjectives do not take adjective endings.

So:

• Mein Zuhause ist ruhig.
• Das Zimmer ist groß.
• Die Kinder sind müde.

But before a noun, adjective endings do appear:

• ein ruhiges Zuhause
• ein großes Zimmer
• müde Kinder

That is why ruhig stays in its basic form here.

Yes, you can, but it may sound a little different.

• Mein Haus ist ruhig focuses more on the house/place
• Mein Zuhause ist ruhig focuses more on your home as your living environment

Both are possible, but Zuhause often sounds more natural if you mean home rather than the physical building.

Sometimes, but not always.

• ruhig often means quiet, calm, or peaceful
• still often means silent or completely quiet

So:

• Mein Zuhause ist ruhig suggests a calm, quiet home
• Mein Zuhause ist still can sound more like there is no sound at all, and in some contexts it may even feel slightly unnatural or dramatic

For describing a pleasant home environment, ruhig is usually the more natural choice.

It sounds completely natural and simple.

The stress would often fall on Zuhause or ruhig, depending on what you want to emphasize:

• Mein Zuhause ist ruhig.
• Mein Zuhause ist ruhig.

If you are just saying it neutrally, the sentence has a calm, everyday feel.

A rough guide:

• Zuhause ≈ tsoo-HOW-zuh
• ruhig ≈ ROO-ikh or in many accents closer to ROO-ig

A few pronunciation notes:

• z in German sounds like ts
• au sounds like ow in how
• h in ruhig helps separate the vowel sounds
• the final g in ruhig is often not pronounced like a hard English g

Pronunciation can vary a little by region, but those rough guides will get you close.