Der Schnuller liegt auf dem Sofa, und das Baby sucht ihn schon.

German nouns have grammatical gender, and you have to learn each noun with its article.

• der Schnuller is masculine
• das Baby is neuter

This does not necessarily match natural gender. A Baby can be a boy or a girl, but the noun Baby is still grammatically neuter.

That grammatical gender matters later in the sentence, especially for pronouns and case endings.

Ihn is the accusative masculine singular pronoun, meaning him/it.

It refers back to der Schnuller:

• nominative: der Schnuller
• accusative pronoun: ihn

So:

• Das Baby sucht ihn. = The baby is looking for it.

Even though ihn often means him in English, here it refers to a thing, because Schnuller is a masculine noun in German.

Because this sentence describes location, not movement.

The two-way preposition auf can take:

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

Here, the pacifier is already lying there:

• auf dem Sofa = on the sofa → location → dative

Compare:

• Der Schnuller liegt auf dem Sofa. = It is on the sofa.
• Ich lege den Schnuller auf das Sofa. = I put the pacifier onto the sofa.

Also, Sofa is a neuter noun:

• nominative: das Sofa
• dative: dem Sofa

Liegen is the normal verb for something that is lying or resting in a horizontal position.

So Der Schnuller liegt auf dem Sofa is very natural German.

German often uses specific position verbs where English might simply use is:

• liegen = lie
• stehen = stand
• sitzen = sit
• hängen = hang

For an object like a pacifier on a sofa, liegt is the best choice.

Because suchen can directly take an object in the accusative.

So this is completely normal:

• Das Baby sucht ihn.

German often does this where English uses a preposition:

• English: look for it
• German: es/ihn suchen

You can also hear nach ihm suchen, and that is not wrong. But the direct-object version is very common and simple.

So:

• Das Baby sucht ihn. = very natural
• Das Baby sucht nach ihm. = also possible

Here schon means something like already or by now.

So the idea is that the baby is already looking for it.

It often adds a sense that something has begun sooner than expected, or that it is happening at this point already.

In this sentence:

• Das Baby sucht ihn schon. = The baby is already looking for it.

This is a normal main clause word order in German.

German main clauses usually put the finite verb in second position:

• das Baby = first element
• sucht = finite verb in second position
• ihn schon = the rest of the clause

So after und, you get another main clause:

• und das Baby sucht ihn schon

Also, object pronouns like ihn often come fairly early in the clause, so this order sounds natural.

Yes, but moving it changes the emphasis.

The given version:

• Das Baby sucht ihn schon.

is very natural and neutral.

If you change the order, the sentence can sound more marked:

• Das Baby sucht schon ihn.
  This sounds contrastive, as if you mean it is already looking for him/it specifically.

So the original placement is the best basic version for learners.

Usually, no. In standard German, a comma before und is often not required when it connects two main clauses.

So many people would simply write:

• Der Schnuller liegt auf dem Sofa und das Baby sucht ihn schon.

The version with the comma is not shocking, but in a simple sentence like this, omitting it is more typical.