Das Kreuz ist sichtbar.

Because Kreuz is a neuter noun in German, so its nominative singular article is das.

German nouns have grammatical gender:

• der = masculine
• die = feminine
• das = neuter

So:

• das Kreuz = the cross

You simply have to learn the noun together with its article.

It is in the nominative case, because it is the subject of the sentence.

In Das Kreuz ist sichtbar:

• Das Kreuz = the thing being talked about
• ist = is
• sichtbar = visible

So das Kreuz is the subject, and subjects are normally in the nominative.

This is standard German main-clause word order:

• subject: Das Kreuz
• verb: ist
• complement: sichtbar

German main clauses usually place the conjugated verb in the second position. Here, the subject comes first, so the verb follows it:

• Das Kreuz | ist | sichtbar

This is very similar to English:

• The cross | is | visible

Ist is the third-person singular form of sein (to be).

The subject das Kreuz is:

• third person
• singular

So the correct form is:

• ich bin
• du bist
• er / sie / es ist

Because das Kreuz is a singular thing, German uses ist.

Sichtbar is an adjective meaning visible.

In this sentence, it comes after the verb ist, so it is being used predicatively. That means it describes the subject through the verb to be.

Compare:

• Das Kreuz ist sichtbar. = The cross is visible.
• ein sichtbares Kreuz = a visible cross

In the second example, the adjective is placed before the noun, so it takes an ending: sichtbares.
But after ist, it stays in its basic form: sichtbar.

Because adjectives in German do not take endings when they come after verbs like sein, werden, or bleiben.

So:

• Das Kreuz ist sichtbar. ✅
• not Das Kreuz ist sichtbares. ❌

Adjective endings only appear when the adjective comes before a noun:

• das sichtbare Kreuz = the visible cross

This is a very common pattern in German.

A rough English guide is kroyts.

More specifically:

• Kr = like English kr
• eu in German often sounds like oy
• z in German is usually pronounced ts

So:

• Kreuz ≈ kroyts

Also, sichtbar is roughly:

• ZIKHT-bar
  where ch is the German sound made in the back of the mouth, not like English ch in chair.

Because all German nouns are capitalized.

So:

• das Kreuz
• der Tisch
• die Stadt

This is one of the most noticeable spelling rules in German. Since Kreuz is a noun, it must begin with a capital letter.

Yes. Those are different ways to express a similar idea, but they are not exactly identical in tone.

• Das Kreuz ist sichtbar. = The cross is visible.
  Focuses on the state or condition of the cross.

• Man sieht das Kreuz. = One sees / You can see the cross.
  Focuses more on the act of seeing it.

• Das Kreuz kann man sehen. = The cross can be seen.
  Also possible, but slightly different in structure and emphasis.

So ist sichtbar is often the most natural way to describe visibility as a condition.

Yes, indirectly.

It is related to the idea of sight/seeing:

• sehen = to see
• sichtbar = visible

A helpful way to think about sichtbar is:

• sicht- relates to sight/visibility
• -bar is a suffix that often means able to be or capable of being

So sichtbar literally has the sense of able to be seen.

Yes, it can be either, depending on context.

Literally:

• a physical cross is visible

Symbolically:

• a cross symbol is visible
• the sign of the cross is visible
• a cross-shaped mark is visible

German Kreuz can refer to several kinds of cross, just like English can. The exact meaning depends on the situation.

Yes, if you mean a cross rather than the cross.

• Das Kreuz ist sichtbar. = The cross is visible.
• Ein Kreuz ist sichtbar. = A cross is visible.

This changes definiteness:

• das = a specific cross already known from context
• ein = any one cross, not previously identified

Both are grammatically correct, but they mean slightly different things.

Yes, that is grammatically possible, but it sounds more marked or stylistic.

German allows different elements to come first, as long as the conjugated verb stays in the second position:

• Das Kreuz ist sichtbar. = neutral, normal
• Sichtbar ist das Kreuz. = emphasizes visible

The second version might be used for contrast or dramatic effect, but the first is the usual basic sentence.