Unter der Rutsche liegt Sand auf dem Boden.

German often puts a location or time expression first to set the scene. Starting with Unter der Rutsche means something like Under the slide, ...

This changes the emphasis, not the basic meaning. The sentence could also be:

Sand liegt unter der Rutsche auf dem Boden.

That sounds more neutral. In the original sentence, the speaker is first telling you where to look.

Because in a main clause, German normally puts the finite verb in second position.

So in:

Unter der Rutsche | liegt | Sand auf dem Boden

the first position is taken by the whole phrase Unter der Rutsche, and the verb must come next. The subject Sand comes after the verb.

This is very common in German:

• Heute kommt er.
• Im Garten spielen die Kinder.
• Unter der Rutsche liegt Sand.

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

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

Here, the sentence describes where the sand is, not movement. So German uses the dative:

• unter der Rutsche = under the slide (location)

If there were movement, you would use accusative:

• Ich lege den Ball unter die Rutsche. = I put the ball under the slide.

For the same reason: auf is also a two-way preposition.

Here it describes location, so it takes the dative:

• auf dem Boden = on the ground/floor

Compare:

• Der Ball liegt auf dem Boden. = location
• Ich lege den Ball auf den Boden. = movement onto the ground

So both unter der Rutsche and auf dem Boden are dative because both describe where something is.

Sand is in the nominative case because it is the subject of the sentence — the thing that lies there.

You can tell because the verb agrees with it:

• Sand liegt ...
  not
• Sand liegen ...

Even though Sand comes after the verb, it is still the subject.

Because Sand is being used as a mass noun in a general sense, like water, milk, or grass.

German often leaves out the article with mass nouns when speaking generally:

• Wasser ist kalt.
• Milch ist im Kühlschrank.
• Sand liegt unter der Rutsche.

You could add an article in some contexts, but it changes the feel:

• Der Sand = the sand, specific sand already known
• Ein Sand is generally not natural here

So in this sentence, Sand without an article is the normal choice.

German often prefers a position verb where English would simply use is.

liegen means to lie or to be lying, and it is used for things that are:

• resting horizontally
• located somewhere as a physical object or substance

So:

• Der Schlüssel liegt auf dem Tisch.
• Das Buch liegt auf dem Bett.
• Sand liegt auf dem Boden.

You could say Da ist Sand, but liegt is more descriptive and more natural when talking about something physically resting on a surface.

No. In German, liegen is used very often for objects and substances too.

Examples:

• Das Buch liegt auf dem Tisch.
• Die Kleidung liegt auf dem Stuhl.
• Schnee liegt auf den Bergen.
• Sand liegt auf dem Boden.

For people, liegen can also mean to be lying down:

• Er liegt im Bett.

So it is much broader than English lie may feel.

Because in German, all nouns are capitalized.

So:

• die Rutsche = the slide
• der Boden = the ground/floor
• der Sand = the sand

This is one of the easiest ways to spot nouns in German sentences.

From the forms in the sentence, you can work it out:

• die Rutsche is feminine
  In dative singular, die becomes der
  So: unter der Rutsche

• der Boden is masculine
  In dative singular, der becomes dem
  So: auf dem Boden

So the dictionary forms are:

• die Rutsche
• der Boden

Yes. They describe two different location relationships:

• unter der Rutsche = relative to the slide
• auf dem Boden = relative to the ground

So the sentence tells you both:

1. the sand is under the slide
2. the sand is on the ground

That is not redundant. It gives a more precise picture.

It is understandable and not impossible, but liegt is more natural here.

Using ist simply says that sand exists/is there:

• Unter der Rutsche ist Sand.

Using liegt emphasizes the sand as a substance resting on a surface:

• Unter der Rutsche liegt Sand auf dem Boden.

So ist is possible in some contexts, but liegt is the better choice in this sentence.

A helpful way to understand it is:

Sand liegt unter der Rutsche auf dem Boden.

That shows the core structure more clearly:

• Sand = subject
• liegt = verb
• unter der Rutsche = location
• auf dem Boden = location

The original sentence moves Unter der Rutsche to the front for emphasis, but the grammar still follows the rule that the verb stays in second position.