Der Lippenstift liegt neben dem Parfüm, und die Handcreme steht vor dem Spiegel.

German often uses different verbs for an object’s position, not just a general verb like to be.

• liegen = to lie, to be lying
• stehen = to stand, to be standing

So the sentence imagines:

• the lipstick is lying next to the perfume
• the hand cream is standing upright in front of the mirror

If the lipstick were upright, steht could also be possible. German is often more specific than English here.

Because both nouns come after prepositions that require the dative here.

The basic forms are:

• das Parfüm → dem Parfüm
• der Spiegel → dem Spiegel

So the article changes because of case, not because the noun’s gender changes.

neben and vor are two-way prepositions. They can take either dative or accusative.

Use:

• dative for location: where something is
• accusative for movement toward a place: where something is going

In this sentence, the objects are already in place, so German uses dative:

• neben dem Parfüm
• vor dem Spiegel

Compare:

• Der Lippenstift liegt neben dem Parfüm.
  The lipstick is next to the perfume.

• Ich lege den Lippenstift neben das Parfüm.
  I put the lipstick next to the perfume.

And:

• Die Handcreme steht vor dem Spiegel.
• Ich stelle die Handcreme vor den Spiegel.

Because each noun has its own grammatical gender, which you usually have to learn with the noun:

• der Lippenstift
• die Handcreme
• das Parfüm
• der Spiegel

Sometimes there is a clue. For example, Handcreme is feminine because its main word is die Creme. But in general, gender is something learners memorize along with the noun.

Because German regularly forms compound nouns by joining words together.

• Hand
  • Creme = Handcreme

This is very normal in German. English often writes such expressions as two words, but German usually makes one noun.

A useful rule: in a compound noun, the last part is the main part, and it determines the gender.

• die Creme → die Handcreme

Because both parts are main clauses, and in German main clauses the finite verb normally comes in second position.

Structure:

• Der Lippenstift | liegt | neben dem Parfüm
• die Handcreme | steht | vor dem Spiegel

The word und connects two main clauses, but it does not send the verb to the end.

The verb goes to the end in a subordinate clause, for example after weil or dass:

• ..., weil die Handcreme vor dem Spiegel steht.

Not necessarily. In a sentence like this, the comma before und is often optional.

So both of these are acceptable:

• Der Lippenstift liegt neben dem Parfüm und die Handcreme steht vor dem Spiegel.
• Der Lippenstift liegt neben dem Parfüm, und die Handcreme steht vor dem Spiegel.

Writers sometimes include the comma to make the sentence structure clearer, especially when two full clauses are joined.

Yes, that would be grammatical:

• Der Lippenstift ist neben dem Parfüm.
• Die Handcreme ist vor dem Spiegel.

But it is less specific. German often prefers position verbs like liegen, stehen, and hängen when the physical position is clear.

So ist is possible, but liegt and steht sound more natural and descriptive here.

Because in German, all nouns are capitalized.

That is why you see:

• Lippenstift
• Parfüm
• Handcreme
• Spiegel

This is a standard spelling rule in German, unlike English, where common nouns are usually not capitalized.

Yes. German word order is flexible, as long as the finite verb stays in second position in a main clause.

So these are both correct:

• Die Handcreme steht vor dem Spiegel.
• Vor dem Spiegel steht die Handcreme.

The difference is emphasis:

• Die Handcreme first emphasizes the object
• Vor dem Spiegel first emphasizes the location

German often moves the first element to highlight what feels most important.

They are in the nominative case because they are the subjects of the two clauses.

• Der Lippenstift liegt ...
• die Handcreme steht ...

They are the things doing the lying and standing, so they appear in nominative form.

That is why you have:

• der Lippenstift, not den Lippenstift
• die Handcreme, which looks the same in nominative and accusative singular, but here it is nominative