Learn Hardcore Croatian: Njezin prijatelj sanja da bude urednik rječnika za hrvatski jezik. - Her friend dreams of being the editor of a dictionary for the Croatian language.

The gender in njezin / njegov refers to the possessor, not to the word prijatelj.
So we know that the friend belongs to a female person (her), not a male person (his).

What is the difference between njezin and njen?

They both mean her, but:

njezin is the standard and more formal form.
njen is very common in everyday speech and informal writing.

In careful or formal Croatian (especially in writing, school, news), you will usually see njezin prijatelj.
In casual conversation, you will very often hear njen prijatelj.

Why do we say sanja da bude and not something like sanja biti urednik?

Croatian generally does not use the infinitive after verbs like želeti / željeti (to want), nadati se (to hope), planirati (to plan), sanjati (to dream) in the same way English uses to + verb.

Instead, Croatian normally uses:

da + present tense

So where English says:

He dreams *of being an editor…*

Croatian says:

Sanja da bude urednik…
(literally: He dreams that he be / will be an editor…)

Using an infinitive here (sanja biti urednik) sounds unnatural or archaic in standard Croatian. The normal, living pattern is sanjati da + present.

What exactly does bude express here, and how is it different from je or će biti?

In da-clause constructions, bude functions like a kind of subjunctive / desired or future state:

da bude urednik ≈ that he (may) be an editor / that he will be an editor

Differences:

da je urednik
Suggests a present/reality idea: that he is an editor (as a fact, now).
da bude urednik
Suggests an unreal, future, or wished-for state: that he would be / will be an editor.
da će biti urednik
Emphasizes a predicted future event: that he will be an editor (more factual, like a prediction).

So in this sentence, bude nicely fits the idea of a wish or dream about the future, not about the present reality.

Can I say sanja o tome da bude urednik rječnika instead of sanja da bude urednik rječnika?

You can, and both are grammatically correct, but there is a nuance:

sanja da bude urednik rječnika
Very direct: He dreams that he will be an editor of a dictionary.
This is the most straightforward and common pattern with sanjati in this meaning “to dream / to aspire”.
sanja o tome da bude urednik rječnika
Literally: He dreams about (the fact) that he will be an editor of a dictionary.
This sounds a bit more talkative/wordy, and brings attention to the idea or topic of that dream.

In everyday speech, Croatian speakers will typically just say sanja da bude…, without o tome.

Why is rječnika in the genitive case here?

Rječnika is the genitive singular of rječnik (dictionary).

The phrase urednik rječnika literally means editor of a dictionary.
When one noun specifies another (editor of what? → of a dictionary), Croatian usually uses the genitive case for the second noun.

So:

urednik rječnika = editor of a dictionary
urednik časopisa = editor of a magazine
autor knjige = author of a book

Using nominative (urednik rječnik) would be ungrammatical here. The relationship “X of Y” is normally shown by Y in the genitive.

Why is za hrvatski jezik in the accusative? Could we also say hrvatskog jezika?

The preposition za always takes the accusative case when it means for:

za hrvatski jezik = for the Croatian language (accusative)

So:

hrvatski jezik is accusative here (same form as nominative for this noun).
That is required by za.

You could express a similar idea using a genitive construction, but the structure would change:

urednik hrvatskog jezika rječnika – this sounds awkward and is not natural.
More natural would be something like urednik hrvatskog rječnika = editor of a Croatian dictionary.

So:

With za, you must use accusative: za hrvatski jezik.
With a noun–noun relationship (X of Y), you typically use genitive: hrvatskog jezika, rječnika, etc.

Can we drop jezik and just say za hrvatski?

Yes, in context you can.

If it is clear that you are talking about languages, za hrvatski will be understood as za hrvatski jezik:

urednik rječnika za hrvatski – editor of a dictionary for Croatian (language)

This is quite natural in speech.
In more formal or careful writing, you will more often see the full za hrvatski jezik, especially when the phrase appears in isolation and the context is not obvious.

How flexible is the word order in this sentence?

Croatian word order is relatively flexible because case endings show grammar roles, but not all orders sound natural.

Your sentence:

Njezin prijatelj sanja da bude urednik rječnika za hrvatski jezik.
is the most natural, neutral order.

Some acceptable variations (with slightly different emphasis) could be:

Njezin prijatelj sanja da bude urednik za hrvatski jezik rječnika. – sounds odd; splitting rječnika from its qualifier is unnatural.
Njezin prijatelj sanja da bude urednik za hrvatski jezik rječnika is better as
Njezin prijatelj sanja da bude urednik rječnika za hrvatski jezik.

You might move the subordinate clause as a whole in more complex contexts, but inside the phrase urednik rječnika za hrvatski jezik, the most natural order is exactly that:
[urednik] [rječnika] [za hrvatski jezik].

How would the sentence change if the friend were female?

You would normally change both prijatelj and urednik to their feminine forms, and adjust njezin accordingly:

Njezina prijateljica sanja da bude urednica rječnika za hrvatski jezik.

Changes:

njezina – feminine form agreeing with prijateljica
prijateljica – female friend
urednica – female editor

(Again, in everyday speech many people would say njena prijateljica, but njezina prijateljica is the standard form.)

Is there any difference in meaning between sanja da bude urednik rječnika and sanja da bude urednik rječnika za hrvatski jezik?

Yes, the longer version is more specific:

sanja da bude urednik rječnika
He dreams of being a dictionary editor (of some dictionary, language not specified).
sanja da bude urednik rječnika za hrvatski jezik
He dreams of being a dictionary editor for the Croatian language in particular.

So the second version adds the information which kind of dictionary he wants to edit.

Does sanja refer only to dreams during sleep, or also to wishes and ambitions?

Sanjati is used for both:

Literal dreams during sleep:
- Noću sanjam čudne snove. – At night I dream strange dreams.
Aspirations / wishes / ambitions:
- Sanja da bude urednik rječnika. – He dreams of being a dictionary editor.
- Sanjam da ću živjeti na moru. – I dream of living at the seaside.

In your sentence, sanja clearly refers to an ambition or life dream, not to a night dream. Context usually makes this clear.