Der Ast über dem Busch bewegt sich im Wind, und die Wurzel bleibt nach dem Regen trotzdem sichtbar.

German nouns have grammatical gender, so each noun takes a specific article:

• der Ast = masculine
• die Wurzel = feminine
• der Busch = masculine
• der Wind = masculine
• der Regen = masculine

This is something you usually have to learn together with the noun. It does not always match natural gender or English logic.

A good habit is to memorize nouns as a unit:

• der Ast
• die Wurzel
• der Busch

Because über is a two-way preposition. That means it can take either:

• dative for a location
• accusative for a direction or movement toward somewhere

Here, über dem Busch means above the bush in a static sense: the branch is located there.

So:

• über dem Busch = above the bush, positioned there
• über den Busch = over/onto the bush, implying movement toward or across it

Even though the branch is moving in the wind, its basic location is still being described, so German uses the dative.

Because Busch is masculine, and after a dative preposition it takes the dative singular article:

• nominative: der Busch
• dative: dem Busch

Since über here requires the dative, der Busch becomes dem Busch.

Sich bewegen is the standard German way to say to move in the sense of to be in motion.

So:

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

The verb is often used reflexively, which means it includes a reflexive pronoun:

• ich bewege mich
• du bewegst dich
• er/sie/es bewegt sich

English often just says move, but German frequently uses sich bewegen.

Im is just the contraction of in dem:

• in dem → im

So:

• im Wind = in the wind

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

The preposition nach can mean after when talking about time.

So:

• nach dem Regen = after the rain

Also, nach always takes the dative, which is why you get:

• dem Regen rather than der Regen or den Regen

No. Nach requires the dative case, and Regen is masculine singular.

That gives:

• nominative: der Regen
• dative: dem Regen

So the correct form is:

• nach dem Regen

Trotzdem means nevertheless, all the same, or despite that.

In this sentence, it adds the idea that even after the rain, the root is still visible:

• ... bleibt nach dem Regen trotzdem sichtbar.
• ... remains visible after the rain nevertheless / all the same.

It does not govern a case like a preposition would. It is an adverb.

That is different from trotz, which is a preposition:

• trotz des Regens = despite the rain

So:

• trotzdem = adverb
• trotz + noun = preposition

Because sichtbar is being used as a predicate adjective, not as an adjective directly before a noun.

After verbs like:

• sein (to be)
• bleiben (to remain)
• werden (to become)

the adjective normally stays in its basic form.

So:

• Die Wurzel bleibt sichtbar. = The root remains visible.

Compare:

• die sichtbare Wurzel = the visible root
  Here, the adjective comes before the noun, so it needs an ending.
• Die Wurzel ist sichtbar.
  Here, it does not.

Bleiben is often used as a linking verb meaning to remain or to stay.

So:

• Die Wurzel bleibt sichtbar. = The root remains visible.

This is a very common German structure:

• Das Haus bleibt leer. = The house remains empty.
• Er bleibt ruhig. = He remains calm.

It connects the subject to a description, just like is or remains in English.

German word order is flexible, but adverbials are often placed in a natural information order.

Here:

• bleibt nach dem Regen trotzdem sichtbar

This sounds natural because it first gives the time context (after the rain) and then adds the contrast (nevertheless) before the final description (visible).

You could sometimes rearrange adverbs in German, but not every version sounds equally natural.

Because both parts are main clauses, and German main clauses normally follow the verb-second rule.

Clause 1:

• Der Ast | bewegt | sich im Wind

Clause 2:

• die Wurzel | bleibt | nach dem Regen trotzdem sichtbar

In each main clause, the finite verb comes in the second position.

In German, all nouns are capitalized, not just proper names.

So in this sentence:

• Ast
• Busch
• Wind
• Wurzel
• Regen

are all capitalized because they are nouns.

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

The comma is there because the sentence joins two full clauses:

• Der Ast über dem Busch bewegt sich im Wind
• die Wurzel bleibt nach dem Regen trotzdem sichtbar

In German, a comma before und is often omitted, but it can be used when two complete clauses are joined and the writer wants clearer structure or a slight pause. So this comma is understandable and natural here.

Yes. What matters is what kind of relationship the preposition expresses, not just whether any motion exists somewhere in the sentence.

• über dem Busch describes where the branch is located: above the bush
• im Wind describes the setting or medium: in the wind

The branch is moving, but it is not moving toward the bush or into the wind in the way German would mark with an accusative destination. So location wording still makes sense.