Wohin hast du den Schnuller gelegt? Ich finde ihn weder im Kinderbett noch im Hochstuhl.

Because wohin asks about direction or destination: to where?

• Wo = where? for a static location
• Wohin = where to? for movement toward a place

Here, the speaker is asking where someone put the pacifier, so the important idea is movement to a location:

• Wohin hast du den Schnuller gelegt? = Where did you put the pacifier?

If you were only asking where it is now, you would normally use wo:

• Wo ist der Schnuller? = Where is the pacifier?

This is the Perfekt tense, which is very commonly used in spoken German to talk about the past.

The pattern is:

• haben
  • past participle

So:

• hast = auxiliary verb from haben
• gelegt = past participle of legen

Together:

• hast ... gelegt = have put / did put

German main-clause word order puts the conjugated verb in second position, so in a question the finite verb comes first:

• Wohin hast du den Schnuller gelegt?

And the past participle usually goes to the end.

Because Schnuller is the direct object of legen, and direct objects usually take the accusative case.

The noun is masculine:

• nominative: der Schnuller
• accusative: den Schnuller

So:

• der Schnuller = the pacifier, as subject
• den Schnuller = the pacifier, as object

Here, you are the subject, and the pacifier is the thing being put somewhere, so German uses the accusative:

• du hast den Schnuller gelegt

For the same reason: the pacifier is the object of finden, not the subject.

• er = nominative masculine pronoun = he/it as subject
• ihn = accusative masculine pronoun = him/it as object

So:

• Er ist im Kinderbett. = It is in the crib.
• Ich finde ihn nicht. = I can’t find it.

In the sentence:

• Ich finde ihn weder im Kinderbett noch im Hochstuhl.

the speaker is finding or not finding it, so German uses ihn.

Weder ... noch means neither ... nor.

So:

• weder im Kinderbett noch im Hochstuhl = neither in the crib nor in the high chair

It links two negative alternatives.

Examples:

• Ich trinke weder Kaffee noch Tee. = I drink neither coffee nor tea.
• Er ist weder zu Hause noch im Büro. = He is neither at home nor in the office.

It is a fixed pairing, so when you use weder, you normally also use noch later in the sentence.

Because the second sentence is about location, not movement.

German often uses:

• in + accusative for movement into something
• in + dative for being inside something

Compare:

• Du legst den Schnuller ins Kinderbett. = You put the pacifier into the crib.
  
  • movement → accusative
• Der Schnuller ist im Kinderbett. = The pacifier is in the crib.
  
  • location → dative

In your sentence, the speaker says where they cannot find it, so this is a location idea:

• im Kinderbett
• im Hochstuhl

Also, im is just a contraction of in dem.

This is a very common German distinction.

• legen = to lay / to put something somewhere
  
  • usually takes an object
  • action done by someone
• liegen = to lie / to be lying somewhere
  
  • no direct object
  • describes position

Examples:

• Ich lege den Schnuller ins Kinderbett. = I put the pacifier into the crib.
• Der Schnuller liegt im Kinderbett. = The pacifier is lying in the crib.

So in your sentence, gelegt is correct because someone actively put the pacifier somewhere.

Because this is a direct question.

In German yes/no questions and wh-questions, the conjugated verb usually comes very early:

• question word + conjugated verb + subject + rest

So:

• Wohin
  • hast
    • du
      • den Schnuller
        • gelegt

That is normal German question word order.

Compare with a statement:

• Du hast den Schnuller ins Kinderbett gelegt.

But as a question:

• Wohin hast du den Schnuller gelegt?

Yes, Schnuller is masculine: der Schnuller.

Unfortunately, grammatical gender in German often has to be learned together with the noun. It is best to memorize nouns with their article:

• der Schnuller
• das Kinderbett
• der Hochstuhl

That will help you produce the right case forms later:

• den Schnuller
• im Kinderbett
• im Hochstuhl

Learning the noun without its article usually makes German much harder.

Gelegt is the past participle of legen.

The basic forms are:

• infinitive: legen
• simple past: legte
• past participle: gelegt

In the Perfekt, German uses the past participle with haben:

• ich habe gelegt
• du hast gelegt

So:

• Wohin hast du den Schnuller gelegt?

Literally, it is something like Where have you put the pacifier?, though in natural English it is often simply Where did you put the pacifier?

Yes, but weder ... noch is the more natural and compact structure for neither ... nor.

Compare:

• Ich finde ihn weder im Kinderbett noch im Hochstuhl.
• Ich finde ihn nicht im Kinderbett und nicht im Hochstuhl.

The second version is understandable, but it sounds heavier and less elegant. Native speakers would usually prefer weder ... noch here.

Because weder ... noch already carries the negative meaning by itself.

So:

• Ich finde ihn weder im Kinderbett noch im Hochstuhl.

already means the speaker cannot find it in either place. You do not need an extra nicht there.

German allows different negative structures, but weder ... noch is a complete and standard one on its own.