Die Verhandlung ist im Gerichtssaal.

Because Verhandlung is a feminine noun, and here it is the subject of the sentence, so it is in the nominative case. The nominative singular definite article for feminine nouns is die.

So:

• die Verhandlung = feminine singular, nominative

A very helpful clue is the ending -ung. In German, nouns ending in -ung are almost always feminine.

Examples:

• die Verhandlung
• die Zeitung
• die Meinung
• die Rechnung

So if you see a noun ending in -ung, it is usually safe to assume it takes die.

Im is simply the common contraction of in dem.

So:

• in dem → im

Both are grammatically correct, but im is much more natural in normal speech and writing.

So:

• Die Verhandlung ist im Gerichtssaal. = normal
• Die Verhandlung ist in dem Gerichtssaal. = also correct, but often sounds more specific or emphasized

Because Gerichtssaal is a masculine noun, and after in it is in the dative here.

The full form is:

• in dem Gerichtssaal

And dem is the dative singular definite article for masculine nouns.

So the pattern is:

• masculine dative singular: dem
• in dem Gerichtssaal → im Gerichtssaal

Because the preposition in can take either accusative or dative, depending on meaning.

Use:

• dative for location = where something is
• accusative for direction/movement = where something is going

Here, the sentence describes a location:

• the hearing/trial is in the courtroom

So German uses dative:

• im Gerichtssaal

Compare:

• Die Verhandlung ist im Gerichtssaal. = location
• Sie gehen in den Gerichtssaal. = movement into the courtroom

Because in den Gerichtssaal would suggest motion toward the courtroom, not being located there.

German makes an important distinction:

• wo? = where? → dative
• wohin? = where to? → accusative

This sentence answers where?, so it uses dative:

• im Gerichtssaal

If you said:

• Sie gehen in den Gerichtssaal that would mean someone is going into the courtroom.

Ist is the 3rd person singular present tense of sein = to be.

It links the subject to the location:

• Die Verhandlung = subject
• ist = is
• im Gerichtssaal = in the courtroom

So ist works just like is in English.

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

In this sentence:

1. Die Verhandlung = first element
2. ist = verb in second position
3. im Gerichtssaal = rest of the sentence

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

For example:

• Die Verhandlung ist im Gerichtssaal.
• Heute ist die Verhandlung im Gerichtssaal.

Even when another element comes first, the conjugated verb still stays in second position.

Because all nouns are capitalized in German.

That is a standard spelling rule:

• die Verhandlung
• der Gerichtssaal

This is different from English, where common nouns are usually not capitalized.

Yes. Gerichtssaal is a compound noun made from:

• Gericht = court
• Saal = hall/room

German very often combines nouns into one longer word. The last part usually tells you the basic type of thing it is:

• Gerichtssaal is a kind of Saal

Also, the grammatical gender usually comes from the last part:

• der Saal → der Gerichtssaal

Yes. That is also a very natural German sentence.

• Die Verhandlung ist im Gerichtssaal. focuses on location in a simple way.
• Die Verhandlung findet im Gerichtssaal statt. is a more idiomatic way to say that the hearing/trial takes place in the courtroom.

Both are correct, but findet ... statt is often especially common for events, meetings, hearings, and similar proceedings.

A few points may help:

• Verhandlung: the h affects the following vowel, and the word has the typical German -ung ending.
• Gerichtssaal: this has a long aa sound in Saal.
• The ch in Gericht is the softer German ch sound, not like English k or ch in church.
• In compounds like Gerichtssaal, the parts are still fairly clear: Gerichts-
  • saal

A learner often benefits from saying the sentence in chunks:

• Die Verhandlung / ist im Gerichtssaal

It is der Gerichtssaal.

So its basic forms are:

• nominative: der Gerichtssaal
• accusative: den Gerichtssaal
• dative: dem Gerichtssaal

That is why after in for location, you get:

• in dem Gerichtssaal → im Gerichtssaal