Der Wein ist kalt.

Because Wein is a masculine noun in German. Its basic article is der.

German nouns have grammatical gender:

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

So the dictionary form is der Wein = wine.

It is both.

In Der Wein ist kalt, der Wein is the subject, and der is also the nominative masculine singular definite article.

Because Wein is masculine and it is the subject of the sentence, der is the correct form.

German main clauses usually follow the verb-second rule, often called V2.

In this sentence:

• Der Wein = first element
• ist = verb in second position
• kalt = the rest

So the structure is: Subject + verb + complement

This is very normal German word order.

Because sein is the infinitive, meaning to be.
Here you need the conjugated form that matches der Wein, which is third person singular.

Conjugation of sein:

• ich bin
• du bist
• er/sie/es ist

Since der Wein is grammatically like er, you use ist.

Because kalt is being used predicatively, after the verb sein.

Compare:

• Der Wein ist kalt. → kalt has no ending
• der kalte Wein → before the noun, the adjective does take an ending

So:

• attributive adjective (before a noun): usually takes an ending
• predicate adjective (after sein, werden, bleiben, etc.): usually has no ending

Yes. That would mean the cold wine is...

Examples:

• Der Wein ist kalt. = The wine is cold.
• Der kalte Wein ist teuer. = The cold wine is expensive.

In the first sentence, kalt describes the wine through the verb ist.
In the second, kalte comes directly before Wein, so it needs an adjective ending.

In German, all nouns are capitalized.

So:

• Wein is a noun, so it is capitalized.
• der is only capitalized here because it is the first word of the sentence.
• ist is a verb, so it is not capitalized.
• kalt is an adjective, so it is not capitalized.

If the article were in the middle of a sentence, it would be lowercase:

• Ich glaube, dass der Wein kalt ist.

Usually no, not in normal standard German.

German generally uses an article more often than English does with singular countable nouns.
So Der Wein ist kalt sounds natural, while Wein ist kalt sounds incomplete in most ordinary contexts.

However, in very special styles—headlines, labels, notes, poetry, or certain general statements—you may sometimes see nouns without an article. But for a standard sentence, use der.

In this sentence, yes, it most naturally means physically cold.

With drinks, kalt means cold/chilled.
So Der Wein ist kalt simply describes the temperature of the wine.

In other contexts, kalt can also have figurative meanings, such as cold in an emotional sense, but that is not the natural reading here.

In a yes/no question, German usually puts the verb first:

Ist der Wein kalt?

So the order becomes:

• Ist = verb first
• der Wein = subject
• kalt = complement

This is the normal pattern for a yes/no question in German.

Wein is pronounced approximately like vine in English.

A rough guide:

• W in German sounds like English v
• ei in German usually sounds like English eye

So:

• Wein ≈ vine

And the full sentence is roughly: dare vine ist kalt

That is only approximate, but it helps as a starting point.