Der erste Tagesordnungspunkt ist kurz, aber der zweite dauert fast eine Stunde.

Because erste and zweite are ordinal numbers, not cardinal numbers.

• eins, zwei, drei = one, two, three
• erste, zweite, dritte = first, second, third

In this sentence, the speaker is talking about the first agenda item and the second one, so German needs ordinal forms.

Examples:

• der erste Punkt = the first point
• der zweite Punkt = the second point

The -e is an adjective ending.

In German, ordinal numbers like erste, zweite, dritte behave like adjectives when they come before a noun. Their endings change depending on:

• the article
• gender
• case
• number

Here we have:

• der erste Tagesordnungspunkt
• der zweite

Tagesordnungspunkt is masculine, and both phrases are in the nominative singular with the definite article der. In that pattern, the adjective ending is -e.

So:

• der erste Punkt
• der zweite Punkt

The noun is masculine because the main noun in the compound is Punkt, and Punkt is masculine: der Punkt.

German compound nouns take their gender from the last element.

So:

• die Tagesordnung = agenda
• der Punkt = point, item
• der Tagesordnungspunkt = agenda item

Since the final part is Punkt, the whole compound is masculine:

• der Tagesordnungspunkt

That is why the sentence says:

• der erste Tagesordnungspunkt
• der zweite

Because German, like English, can leave out a noun when it is already clear from context.

So:

• der erste Tagesordnungspunkt ist kurz
• aber der zweite dauert fast eine Stunde

really means:

• ... aber der zweite Tagesordnungspunkt dauert fast eine Stunde

But repeating the full noun would sound unnecessary. German often uses an adjective or ordinal number with an article as a kind of shorthand when the noun is understood.

Very similar to English:

• the first item is short, but the second lasts almost an hour

Because kurz comes after the verb ist and works as a predicate adjective.

In German, predicate adjectives do not take adjective endings.

Compare:

• ein kurzer Punkt = a short item
  
  • adjective before the noun, so it takes an ending
• der Punkt ist kurz = the item is short
  
  • adjective after ist, so no ending

In the sentence:

• Der erste Tagesordnungspunkt ist kurz

kurz is linked to the subject by ist, so it stays in its basic form.

Because the two parts express different ideas.

• ist kurz describes a quality: it is short
• dauert fast eine Stunde describes duration: it lasts almost an hour

So the speaker is saying:

• the first agenda item is short
• the second one lasts almost an hour

This is very natural German.

You could think of it like this:

• kurz sein = to be short
• eine Stunde dauern = to last an hour

Because aber is a coordinating conjunction. It does not force the verb to move to the end.

German main clauses usually follow the verb-second rule, meaning the finite verb is in the second position.

First clause:

• Der erste Tagesordnungspunkt ist kurz

Second clause after aber:

• der zweite dauert fast eine Stunde

So the pattern is:

• main clause + aber
  • main clause

This is different from subordinating conjunctions like weil, where the verb goes to the end.

Compare:

• ..., aber der zweite dauert fast eine Stunde.
• ..., weil der zweite fast eine Stunde dauert.

Yes, and that is a very common trap for English speakers.

In German, fast usually means almost, not quickly.

So:

• fast eine Stunde = almost an hour

If you want to say quickly, German usually uses:

• schnell

Examples:

• Das geht schnell. = That goes quickly.
• Es dauert fast eine Stunde. = It lasts almost an hour.

So in this sentence, fast does not mean the item happens at high speed. It means the duration is nearly one hour.

Here eine Stunde is in the accusative case, because dauern commonly takes an expression of duration as its object.

So:

• Es dauert eine Stunde. = It lasts an hour.
• Der Film dauert zwei Stunden. = The film lasts two hours.

In your sentence:

• der zweite dauert fast eine Stunde

the phrase eine Stunde tells us how long it lasts.

This is a common pattern with dauern.

Yes. It is a very normal German compound noun.

It is built from:

• Tag
• Ordnung
• Tagesordnung = agenda
• Punkt = point, item

So:

• Tagesordnungspunkt = agenda item / item on the agenda

German often combines words into one long noun where English would use several words.

Other examples:

• Bahnhof = train station
• Haustür = house door / front door
• Arbeitszimmer = study / work room

So even though Tagesordnungspunkt looks long, it follows a very standard German pattern.

It would be:

• Der erste Tagesordnungspunkt ist kurz, aber der zweite Tagesordnungspunkt dauert fast eine Stunde.

This is grammatically correct, but it sounds more repetitive. Native speakers usually prefer:

• Der erste Tagesordnungspunkt ist kurz, aber der zweite dauert fast eine Stunde.

So the version in your sentence is more natural.

A helpful rough breakdown is:

• Ta-ges-ord-nungs-punkt

The stress is mainly on:

• Ta in Tages-
• Ord in Ordnung
• Punkt is also clearly pronounced at the end

A rough English-style guide would be something like:

• TAH-gess-ORD-noongs-punkt

A few pronunciation notes:

• tag in Tages sounds like Tahg, not like English tag
• ordnung has an o sound more like or than English short o
• ung sounds like oong
• punkt has a short u, not like English punk exactly, but somewhat similar

If you say it slowly in chunks, it becomes much easier:

• Tages
  • Ordnung
    • Punkt