Der Ast, auf dem der Vogel sitzt, bewegt sich im Wind.

Because auf dem der Vogel sitzt is a relative clause. In German, relative clauses are set off with commas.

• Main clause: Der Ast bewegt sich im Wind.
• Relative clause: auf dem der Vogel sitzt

The relative clause gives extra information about der Ast, so it gets commas on both sides when it is inserted into the middle of the sentence.

It is describing der Ast.

In English, this is like saying the branch, on which the bird is sitting, ... or more naturally the branch that the bird is sitting on...

So the noun Ast is the thing being described, and the relative clause tells you which branch.

Because dem is the dative form of the relative pronoun.

Here is the logic:

1. The relative clause refers back to der Ast.
2. Ast is masculine singular.
3. The preposition auf can take either accusative or dative.
4. Here it expresses location (on the branch), not movement toward something, so German uses the dative.
5. The dative masculine form is dem.

So:

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

That is why German says auf dem der Vogel sitzt.

Because auf is one of the two-way prepositions. These take:

• accusative for direction/movement toward
• dative for location/position

Here the bird is already sitting on the branch, so this is a location, not a destination.

Compare:

• Der Vogel sitzt auf dem Ast. = The bird is sitting on the branch. → location → dative
• Der Vogel fliegt auf den Ast. = The bird flies onto the branch. → direction → accusative

So auf dem is correct here.

Because in German, a relative clause is a type of subordinate clause, and in subordinate clauses the conjugated verb usually goes to the end.

So:

• relative pronoun: auf dem
• subject: der Vogel
• verb at the end: sitzt

This is normal German word order for subordinate clauses.

Because the main clause is still about Der Ast.

The full structure is:

• Main clause beginning: Der Ast
• Inserted relative clause: auf dem der Vogel sitzt
• Main clause continues: bewegt sich im Wind

If you remove the relative clause, the core sentence is:

Der Ast bewegt sich im Wind.

So after the inserted clause ends, German returns to the main clause and continues normally.

Because sich bewegen is a very common German verb meaning to move.

In this sentence, bewegt sich means the branch is moving by itself, or is swaying.

• Der Ast bewegt sich. = The branch moves / is moving.

Without sich, bewegen is often used more transitively, meaning to move something:

• Der Wind bewegt den Ast. = The wind moves the branch.

So:

• sich bewegen = to move
• etwas bewegen = to move something

Yes. im = in dem.

So:

• im Wind = in dem Wind

This contraction is very common in German and is usually preferred when it sounds natural.

Because der Vogel is the subject of the relative clause, and subjects are in the nominative case.

Inside auf dem der Vogel sitzt:

• der Vogel = subject
• sitzt = verb
• auf dem = prepositional phrase referring to the branch

So der Vogel stays in nominative.

Both, in different ways.

A relative pronoun in German is determined by:

1. gender and number of the noun it refers to
2. case required by its function in the relative clause

Here:

• it refers to der Ast → masculine singular
• it comes after auf in a location phrase → dative

So the correct form is dem:

• masculine singular + dative = dem

This is a very important pattern in German relative clauses.

Yes, that is possible.

• auf dem der Vogel sitzt
• auf welchem der Vogel sitzt

Both are grammatically correct. But auf dem is much more common and natural in everyday German. Welchem sounds more formal or literary.

A useful pattern is:

[noun], [preposition + relative pronoun + subject + verb], [main clause continues].

For example:

• Das Haus, in dem ich wohne, ist alt.
• Der Stuhl, auf dem sie sitzt, ist bequem.
• Der Tisch, an dem wir essen, ist groß.

So your sentence follows a very common German structure: noun + relative clause + main clause.