Die Hälfte ist fertig.

Die is the definite article the.

In die Hälfte, Hälfte is a feminine noun, so it takes die in the nominative singular:

• die Hälfte = the half

Here, die Hälfte is the subject of the sentence, so nominative case is used.

A learner often expects just half without an article because English often says Half is done or Half is ready, but German commonly uses the noun phrase die Hälfte.

Because Hälfte is a noun, and all German nouns are capitalized.

So:

• die Hälfte = noun phrase
• fertig = adjective, so it is not capitalized

This is one of the most noticeable differences from English spelling.

They are related, but they are not used the same way.

• die Hälfte = the half / one half
  This is a noun.
• halb = half
  This is usually an adjective, adverb, or part of expressions.

Examples:

• Die Hälfte ist fertig. = Half is finished / One half is ready.
• Das Glas ist halb voll. = The glass is half full.
• um halb drei = at half past two / at 2:30

So in your sentence, German uses the noun Hälfte, not halb.

Because the subject is die Hälfte, and that is grammatically singular.

Even though half refers to part of something larger, the noun Hälfte itself is singular, so the verb is singular too:

• Die Hälfte ist fertig.

Compare:

• Die Teile sind fertig. = The parts are ready.
• Die Hälfte ist fertig. = Half is ready.

A good shortcut is: the verb agrees with Hälfte, not with the idea of many things in the background.

Because this is a normal German main clause, and German main clauses usually follow the verb-second rule.

The structure is:

• Die Hälfte = position 1
• ist = position 2
• fertig = the rest

So:

• Die Hälfte ist fertig.

This is the standard word order for a simple statement.

Fertig is an adjective.

In this sentence, it comes after sein (ist), so it is being used predicatively. That means it does not take adjective endings.

• Die Hälfte ist fertig.

Compare that with an attributive use, where adjective endings do appear:

• die fertige Hälfte = the finished half

So:

• after sein: fertig
• before a noun: fertige, fertiger, fertiges, etc., depending on the grammar

It can mean either, depending on context.

Common meanings of fertig include:

• finished
• done
• ready

So Die Hälfte ist fertig could mean:

• Half is finished
• Half is done
• Half is ready

The exact English wording depends on the situation:

• If you are building something: Half is finished
• If you are preparing something: Half is ready
• If you are doing a task: Half is done

German often leaves that unstated if the context is already clear.

So Die Hälfte ist fertig can stand on its own if everyone already knows what is being talked about.

If you want to make it explicit, you can add more information:

• Die Hälfte davon ist fertig. = Half of it is ready.
• Die Hälfte der Arbeit ist fertig. = Half of the work is done.
• Die Hälfte der Aufgaben ist fertig. = Half of the tasks is/are done.

So the short sentence is perfectly normal when the reference is understood from context.

Yes, it is natural, especially in context.

For example:

• when talking about a project
• when describing progress
• when saying that one part is complete and the other is not

Examples:

• Wie weit seid ihr? – Die Hälfte ist fertig.
  How far along are you? – Half is done.

• Von der Renovierung ist die Hälfte fertig.
  Half of the renovation is finished.

By itself, the sentence is a little context-dependent, but that is very normal in both German and English.

A rough pronunciation guide is:

• die ≈ dee
• Hälfte ≈ HELF-tuh
• ist ≈ ist
• fertig ≈ FER-tikh or FER-tig depending on accent/region

A few useful notes:

• ä in Hälfte sounds somewhat like the e in bed, though not exactly the same.
• The ft cluster in Hälfte is pronounced clearly.
• In standard pronunciation, the final -ig in fertig is often pronounced like -ich, so FER-tich is common.

Because that is simply part of the word’s standard spelling: Hälfte.

You should learn it as a fixed vocabulary item:

• die Hälfte = half

This matters because changing or omitting the umlaut creates a spelling mistake:

• correct: Hälfte
• incorrect: Halfte

German uses umlauts to distinguish different vowel sounds, and they are not optional.

The plural is die Hälften.

So:

• singular: die Hälfte
• plural: die Hälften

Examples:

• Eine Hälfte ist fertig. = One half is finished.
• Beide Hälften sind fertig. = Both halves are finished.

In your sentence, it is singular, so you use ist.

Yes, but it changes the nuance a little.

• Die Hälfte ist fertig. = The half / Half is finished
  This usually refers to a specific half already known from context.
• Eine Hälfte ist fertig. = One half is finished
  This can sound more like one of the two halves.

So both are possible, but die Hälfte is the more natural default when you mean half of the whole thing.

Yes, but with people it often means something slightly different depending on context.

Examples:

• Ich bin fertig. can mean
  
  • I’m finished
  • I’m done
  • sometimes even I’m exhausted

But in Die Hälfte ist fertig, with a thing or a task, it usually means finished / done / ready, not exhausted.

So the meaning of fertig depends a lot on what it refers to.