Der Junge stolpert über den Ast und fällt auf den Boden.

Because der Junge is the subject of the sentence, so it is in the nominative case. Den Ast is the thing affected by the action stolpert über, so it is in the accusative case.

Both Junge and Ast are masculine nouns, so their definite articles change like this:

• nominative: der
• accusative: den

So:

• der Junge = the boy
• den Ast = the branch

Über is a two-way preposition, which means it can take either:

• accusative for direction/movement toward or across
• dative for location

Here, the expression is über etwas stolpern = to trip over something, and it normally uses the accusative.

So:

• über den Ast stolpern = to trip over the branch

Using über dem Ast would sound like a location idea such as above the branch, which is not what is meant here.

This is another two-way preposition.

With auf:

• auf den Boden = onto the ground/floor → movement toward it
• auf dem Boden = on the ground/floor → already there, location

In the sentence, the boy falls onto the ground, so German uses the accusative:

• auf den Boden

If you said:

• Der Junge liegt auf dem Boden.

that would mean The boy is lying on the ground.

Because fallen is a strong verb, and in the present tense its vowel changes in the 2nd person singular and 3rd person singular.

Present tense:

• ich falle
• du fällst
• er/sie/es fällt
• wir fallen
• ihr fallt
• sie/Sie fallen

So in this sentence, the subject is der Junge = he, so the correct form is fällt.

Because the subject is der Junge, which is 3rd person singular (he).

In the present tense, regular verbs usually take -t in the er/sie/es form:

• ich stolpere
• du stolperst
• er stolpert

And for fallen:

• er fällt

So both verbs agree with the subject der Junge.

Because German, like English, often leaves out the subject in the second part when it is the same subject.

So:

• Der Junge stolpert über den Ast und fällt auf den Boden.

means:

• The boy trips over the branch and falls to the ground.

You could also say:

• Der Junge stolpert über den Ast und der Junge fällt auf den Boden.

but that sounds repetitive and unnatural.

Because und is a coordinating conjunction. It connects two equal parts of a sentence and does not force the verb to move to the end.

Compare:

• Der Junge stolpert über den Ast und fällt auf den Boden.

If the subject is repeated, you get normal word order again:

• Der Junge stolpert über den Ast und er fällt auf den Boden.

So und behaves much like and in English.

Yes. Junge is a weak masculine noun.

Its singular forms are:

• nominative: der Junge
• accusative: den Jungen
• dative: dem Jungen
• genitive: des Jungen

In your sentence, it stays der Junge because it is the subject. But if boy were an object, you would usually see Jungen, for example:

• Ich sehe den Jungen. = I see the boy.

This is a very useful pattern to remember.

Because in German, all nouns are capitalized.

So:

• der Junge
• der Ast
• der Boden

This is one of the most noticeable spelling differences between German and English.

Yes. Boden can mean:

• ground outdoors
• floor indoors

The exact meaning depends on context.

So auf den Boden fallen can mean:

• to fall to the ground
• to fall to the floor

In your sentence, English might translate it either way depending on the situation.

German often uses the present tense to describe actions in a general, vivid, or narrative way, just as English can.

So:

• Der Junge stolpert über den Ast und fällt auf den Boden.

is literally present tense: The boy trips over the branch and falls to the ground.

Depending on context, English might prefer past tense, but grammatically the German sentence is simply in the present.