Für das Projekt in der Schule brauchen wir Kleber, einen Locher und einen Tacker.

Because German is a verb-second language in main clauses.

The sentence begins with Für das Projekt in der Schule, so that whole phrase takes the first position. The conjugated verb must then come second:

• Für das Projekt in der Schule brauchen wir ...

If you started with wir, then you would say:

• Wir brauchen für das Projekt in der Schule ...

Both are correct. The original just puts extra emphasis on for the project at school.

Because für always takes the accusative case.

• das Projekt is a neuter noun: das Projekt
• In the accusative, neuter stays das
• So: für das Projekt

Compare:

• der Tisch → für den Tisch
• die Schule → für die Schule
• das Projekt → für das Projekt

Because here in describes a location, not movement.

German uses:

• in + dative for location: in der Schule = in/at the school
• in + accusative for movement into something: in die Schule = into the school

So:

• Das Projekt ist in der Schule. = location
• Wir gehen in die Schule. = movement

In this sentence, it means the project is connected with school, so der Schule is dative.

Because Kleber is being used as an uncountable material noun here, like glue in English.

So German often says:

• Wir brauchen Kleber. = We need glue.

But Locher and Tacker are countable singular objects, so they need an article:

• einen Locher
• einen Tacker

In some contexts, you might hear einen Kleber, especially if someone means a specific glue stick or glue product, but in this sentence Kleber is more naturally understood as glue in general.

Because both Locher and Tacker are masculine singular nouns, and they are the objects of brauchen, so they are in the accusative.

For masculine nouns:

• nominative: der Locher, der Tacker
• accusative: einen Locher, einen Tacker

That is why the article changes to einen.

• der Locher = hole punch
• der Tacker = stapler

They are both everyday office or school-supply words.

Also useful:

• ein Blatt lochen = to punch holes in a sheet of paper
• etwas tackern = to staple something

Most naturally, it goes with das Projekt:

• the project at school
• or the school project

So the sentence is understood as:

• For the project at school, we need glue, a hole punch, and a stapler.

In real life, listeners usually understand this easily from context. German often allows this kind of phrase placement without needing to make it more explicit.

Yes, absolutely.

That would be a more neutral word order:

• Wir brauchen für das Projekt in der Schule Kleber, einen Locher und einen Tacker.

The original sentence puts Für das Projekt in der Schule first to emphasize the purpose/context.

Both are normal German.

Because in a simple list, German normally does not use a comma before und.

So this is correct:

• Kleber, einen Locher und einen Tacker

German punctuation here works much like standard English without the Oxford comma.

Because in German, all nouns are capitalized.

So:

• das Projekt
• die Schule
• der Kleber
• der Locher
• der Tacker

This is one of the most noticeable spelling rules in German.

Yes, Kleber is usually masculine: der Kleber.

But in this sentence, it is used without an article, as a general substance word:

• Wir brauchen Kleber.

When no article is used, you do not see a case ending on the article, so the gender is less visible on the surface.

If you added an article, then gender and case would matter more clearly, for example:

• Wir brauchen den Kleber. = We need the glue.
• Wir brauchen einen Kleber. = We need a glue / a type of glue / a glue stick (depending on context)

Yes. In many contexts, in der Schule can mean either:

• in the school literally
• at school more naturally in English

German often uses in der Schule where English would prefer at school.

So here, a natural English understanding is:

• for the project at school

Yes, most likely.

The phrase für das Projekt uses the definite article das, so it means:

• for the project

That suggests a specific project already known from context.

If it were any project, German might say:

• für ein Projekt = for a project

So das Projekt sounds specific, while ein Projekt would sound nonspecific.