An der Pinnwand hängen unser Stundenplan und zwei Zettel, die ich mit einer Heftklammer festgemacht habe.

Because German main clauses follow the verb-second rule.

That means:

• the element in first position can be the subject, a time expression, a place expression, etc.
• the finite verb must come in second position

Here, An der Pinnwand takes first position, so hängen has to come next:

• An der Pinnwand | hängen | unser Stundenplan und zwei Zettel

A more neutral subject-first version would be:

• Unser Stundenplan und zwei Zettel hängen an der Pinnwand.

Starting with An der Pinnwand puts a bit more focus on the location.

Because an is a two-way preposition. It can take:

• dative for location
• accusative for movement toward a place

Here the sentence describes where the items already are, so German uses the dative:

• an der Pinnwand = at/on the bulletin board

Compare:

• Die Zettel hängen an der Pinnwand. = location
• Ich hänge die Zettel an die Pinnwand. = movement toward the board

So der Pinnwand is dative because this is a static location.

German usually uses an for things attached to or hanging on a vertical surface.

So:

• an der Wand
• an der Tür
• an der Pinnwand

By contrast, auf is more typical for something resting on top of a surface, especially a horizontal one:

• auf dem Tisch
• auf dem Boden

Since a bulletin board is treated as a vertical surface that things are attached to, an der Pinnwand is the natural choice.

Because the subject is plural overall:

• unser Stundenplan und zwei Zettel

When two noun phrases are joined by und, they form a compound subject, and the verb is normally plural.

So:

• Der Stundenplan hängt ... = singular
• Der Stundenplan und zwei Zettel hängen ... = plural

That is why the sentence has hängen, not hängt.

Because Stundenplan is part of the subject, so it is in the nominative case.

unser works like a determiner, and its ending depends on case, gender, and number.

Here:

• Stundenplan is masculine singular
• it is nominative
• so the correct form is unser Stundenplan

Compare:

• unser Stundenplan = nominative masculine
• unseren Stundenplan = accusative masculine
• unserem Stundenplan = dative masculine

So unseren would be wrong here because the noun is not a direct object.

German often uses specific position/location verbs where English might simply use to be.

Common ones are:

• stehen for things standing upright
• liegen for things lying flat
• hängen for things hanging or being attached

So German prefers:

• Die Zettel hängen an der Pinnwand.

rather than the less specific:

• Die Zettel sind an der Pinnwand.

Using hängen gives a clearer picture of how the objects are positioned.

Here die is a relative pronoun. It introduces a relative clause, which adds extra information about the noun phrase before it.

So the structure is:

• unser Stundenplan und zwei Zettel = the thing being talked about
• die ich mit einer Heftklammer festgemacht habe = extra information about it

In English, this is like that or which.

A useful detail:

• the relative pronoun agrees with its antecedent in number and gender
• its case depends on its role inside the relative clause

Here, die is plural because the thing it refers to is plural. Inside the clause, it functions as the object of festgemacht habe.

Grammatically, die can refer to the whole plural phrase:

• unser Stundenplan und zwei Zettel

because that whole phrase is plural.

So strictly speaking, the relative clause attaches to the entire noun phrase before it.

That said, in real life, listeners may interpret it according to context. If the speaker really wants to make it crystal clear that only the notes were fastened, German would often rephrase the sentence.

So the short answer is:

• grammatically: it refers to the whole plural phrase
• contextually: it may feel like the speaker especially means the papers/notes

Because in German, relative clauses are separated by commas.

So whenever you have a clause like:

• ..., die ich ...
• ..., der wir ...
• ..., das er ...

you normally need a comma before it.

That comma is not optional here.

Because mit always takes the dative case.

The noun Heftklammer is feminine:

• die Heftklammer

Its indefinite article changes in the dative singular:

• eine Heftklammer = nominative/accusative
• einer Heftklammer = dative

So:

• mit einer Heftklammer = with a paper clip / staple

The key point is simply:

• mit + dative

Because this part of the sentence is a relative clause, and German subordinate clauses send the finite verb to the end.

The basic main-clause order would be:

• Ich habe sie mit einer Heftklammer festgemacht.

But inside the relative clause, the verb material moves to the end:

• ..., die ich mit einer Heftklammer festgemacht habe.

Also, festmachen is a separable verb:

• infinitive: festmachen
• past participle: festgemacht

So in the perfect tense, the verb phrase is:

• festgemacht habe

That is why the end of the clause looks the way it does.

festmachen is a separable verb made of:

• fest- = firm, secure, fixed
• machen = to make/do

Together, festmachen means something like:

• to fasten
• to attach
• to secure

Because it is separable:

• present tense main clause: Ich mache den Zettel fest.
• perfect tense: Ich habe den Zettel festgemacht.

So festgemacht is the past participle of festmachen.