Ich suche dieses Wort im Wörterbuch.

Because Wort is a neuter noun in German: das Wort.

So the demonstrative dies- has to match:

• dieser = masculine
• diese = feminine
• dieses = neuter

Since Wort is neuter, you say dieses Wort.

In this sentence, dieses Wort is also in the accusative case, but for neuter singular, dieses stays the same in both nominative and accusative:

• nominative: dieses Wort
• accusative: dieses Wort

It is in the accusative case.

The verb suchen usually takes a direct object, and the thing being searched for is that object:

• Ich suche dieses Wort.

So:

• Ich = subject, nominative
• dieses Wort = direct object, accusative

Because im means in dem, and here it describes a location: where the searching happens.

With in, German uses:

• accusative for movement toward a destination
• dative for location

Here the idea is not into the dictionary as a destination, but in the dictionary as the place where you are searching.

So:

• in dem Wörterbuch → im Wörterbuch

Im is a contraction of in dem.

So:

• im Wörterbuch = in dem Wörterbuch

This kind of contraction is very common in German:

• am = an dem
• im = in dem
• vom = von dem
• zum = zu dem

Because this is a normal main clause, and in German main clauses the finite verb usually goes in second position.

So the pattern is:

• Ich = first element
• suche = second position
• the rest follows

That gives:

• Ich suche dieses Wort im Wörterbuch.

The verb would move toward the end in a subordinate clause, for example:

• ..., weil ich dieses Wort im Wörterbuch suche.

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

For example, these are possible:

• Ich suche dieses Wort im Wörterbuch.
• Im Wörterbuch suche ich dieses Wort.
• Dieses Wort suche ich im Wörterbuch.

They all mean roughly the same thing, but the focus changes:

• Ich suche dieses Wort im Wörterbuch = neutral
• Im Wörterbuch suche ich dieses Wort = emphasizes where
• Dieses Wort suche ich im Wörterbuch = emphasizes which word

Because in German, all nouns are capitalized.

So:

• das Wort
• das Wörterbuch

This is different from English, where common nouns are normally lowercase.

It is understandable and grammatically correct, but many native speakers would more naturally say:

• Ich schlage dieses Wort im Wörterbuch nach.

That verb, nachschlagen, often means to look something up in a reference source such as a dictionary.

So there is a small nuance:

• suchen = to search/look for
• nachschlagen = to look up

Your sentence is fine, but nachschlagen is often the more idiomatic choice when talking about dictionaries.

That is a good question because suchen and nach ... suchen are related, but they are not used in exactly the same way.

Usually:

• etwas suchen = to search for something directly
• nach etwas suchen = to look/search for something

Examples:

• Ich suche mein Handy.
• Ich suche nach meinem Handy.

Both can work, though the second one often feels a bit more like looking around for something.

In your sentence, Ich suche dieses Wort im Wörterbuch is normal because dieses Wort is the direct object of suche.

Suche is the first-person singular present tense form of suchen.

The present tense forms are:

• ich suche
• du suchst
• er/sie/es sucht
• wir suchen
• ihr sucht
• sie/Sie suchen

So Ich suche means I search / I am searching / I look for, depending on context.

There actually is one, but it is hidden inside im.

Since:

• im = in dem

the noun already has the article dem.

So:

• im Wörterbuch already means in the dictionary

That is why you do not add another article.

Here it is singular.

You can tell because:

• im = in dem, and dem is singular here
• the noun form is Wörterbuch

Singular:

• das Wörterbuch

Plural:

• die Wörterbücher

So:

• im Wörterbuch = in the dictionary
• in den Wörterbüchern = in the dictionaries

Because the form tells you it is dative, which usually signals location with in.

Compare:

• Ich bin im Wörterbuch. = I am in the dictionary.
• Ich gehe in das Wörterbuch. = I go into the dictionary.

In real life, the second example is odd semantically, but grammatically it shows the pattern:

• dative = location
• accusative = direction/movement toward

In your sentence, im Wörterbuch clearly expresses location.