Hinter dem Zaun steht ein dichter Strauch, in dem sich oft Vögel verstecken.

Because hinter is a two-way preposition in German. That means it can take:

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

Here the bush is already located behind the fence, so German uses the dative: hinter dem Zaun.

Compare:

• Der Strauch steht hinter dem Zaun. = The bush is behind the fence.
• Ich stelle den Topf hinter den Zaun. = I put the pot behind the fence.

Both are possible. German main clauses follow the verb-second rule: the finite verb must be the second element.

If you put Hinter dem Zaun first for emphasis, the verb must come next:

• Hinter dem Zaun steht ein dichter Strauch.

If you put the subject first, that is also correct:

• Ein dichter Strauch steht hinter dem Zaun.

The version in your sentence emphasizes the location first.

Yes. In German, stehen is often used for things that are upright and in a fixed position, not just for people.

So plants, trees, buildings, fences, bottles, and similar things can all stehen:

• Ein Baum steht im Garten.
• Das Haus steht am See.
• Die Flasche steht auf dem Tisch.

So ein Strauch steht is completely natural German.

dicht here means dense or thick.

So ein dichter Strauch means a dense bush.

The ending -er is there because the adjective describes a masculine noun in the nominative singular after ein:

• noun: der Strauch (masculine)
• case here: nominative because it is the subject
• article: ein
• adjective ending: -er

That is why it is:

• ein dichter Strauch

not:

• ein dicht Strauch

in dem introduces a relative clause and refers back to Strauch.

So:

• ein dichter Strauch, in dem ...

means:

• a dense bush, in which ...

The relative clause gives extra information about the bush.

You can think of it like this:

• main noun: Strauch
• extra information: in dem sich oft Vögel verstecken

So the whole thing means: the bush is the place in which birds often hide.

Because this is a relative pronoun construction, not just a normal article.

• in dem = in which
• im = contraction of in dem, but normally used with the article, not with a relative pronoun

In standard German, relative clauses normally keep the full form:

• der Strauch, in dem ...

not:

• der Strauch, im ...

So here in dem is the correct form.

The relative pronoun has to match the noun it refers to and also take the correct case for its role inside the relative clause.

It refers back to:

• der Strauch → masculine singular

Inside the relative clause, it follows in, and in here describes a location, so it takes the dative.

So you get:

• masculine singular + dative = dem

That is why it is:

• in dem

If it referred to a feminine noun, it would be in der.
If it referred to a plural noun, it would be in denen.

Because sich verstecken means to hide oneself / to hide.

German uses verstecken in two common ways:

• jemanden / etwas verstecken = to hide someone/something
• sich verstecken = to hide oneself

So in this sentence, the birds are not hiding something else. They are hiding themselves:

• Vögel verstecken sich. = Birds hide.

That is why sich is needed.

Because in dem sich oft Vögel verstecken is a subordinate clause—more specifically, a relative clause.

In German subordinate clauses, the finite verb usually goes to the end.

Compare:

• main clause: Vögel verstecken sich oft.
• relative clause: ..., in dem sich oft Vögel verstecken.

So the final position of verstecken is normal German subordinate-clause word order.

German word order in the middle of a clause is more flexible than English, especially in subordinate clauses.

Here:

• in dem sich oft Vögel verstecken

the reflexive pronoun sich comes early, and oft is placed before the full noun Vögel. That is possible and natural.

A more straightforward version would also be:

• in dem sich Vögel oft verstecken

Both are grammatical. The original sentence gives a slightly different flow and emphasis, but the meaning stays the same.

Because German often uses zero article with an indefinite plural.

There is no plural form of ein. So when you mean some birds or birds in general, German often simply says:

• Vögel

not:

• ein Vögel

If the sentence were talking about specific birds already known from context, it could use:

• die Vögel

But here the meaning is general/indefinite: birds often hide in the bush.