Hun staver ordet med ét bogstav ad gangen, fordi udtalen er svær.

Because hun is the subject form, like she in English. In this sentence, she is the one doing the action:

• Hun staver ordet ... = She spells the word ...

Hende is the object form, like her in English.

• Jeg ser hende = I see her

So here, hun is correct.

Because staver is the present tense of the verb at stave = to spell.

In Danish, the present tense is usually formed by adding -r to the infinitive:

• at stave → staver
• at tale → taler
• at læse → læser

So:

• Hun staver ordet = She spells the word / She is spelling the word

Danish present tense often covers both simple present and present progressive English meanings.

Because ordet means the word, while ord means word in a more general or indefinite sense.

• et ord = a word
• ordet = the word

Danish usually adds the definite article to the end of the noun instead of using a separate word like the:

• en bog = a book
• bogen = the book
• et ord = a word
• ordet = the word

So Hun staver ordet means She spells the word.

It is ét because bogstav is a neuter noun:

• et bogstav = a letter

The form ét is the stressed version of et and means one in the sense of a single one.

So:

• et bogstav = a letter
• ét bogstav = one letter

The accent helps show that this is the number one, not just the indefinite article.

Since bogstav is neuter, you use et/ét, not en.

It means with one letter at a time or more naturally in English, one letter at a time.

The phrase breaks down like this:

• med = with
• ét bogstav = one letter
• ad gangen = at a time

So the whole idea is that she spells it slowly, giving each letter separately.

Ad gangen is a fixed expression meaning at a time.

You will often see it with numbers or quantities:

• én ad gangen = one at a time
• to ad gangen = two at a time

In your sentence:

• ét bogstav ad gangen = one letter at a time

It is an idiomatic expression, so it is best learned as a chunk.

Because the phrase is one letter at a time, so singular makes sense.

After ét, Danish uses the singular noun:

• ét bogstav = one letter
• to bogstaver = two letters

So ét bogstav ad gangen literally means one letter at a time, not letters at a time.

Because udtalen means the pronunciation, while udtale means pronunciation in a more general or indefinite sense.

• en udtale = a pronunciation
• udtalen = the pronunciation

Here it refers to the pronunciation of the word being spelled, so Danish uses the definite form:

• fordi udtalen er svær = because the pronunciation is difficult

In English, we might sometimes say because pronunciation is difficult, but Danish more naturally uses the pronunciation here.

Because udtalen is a common-gender noun:

• en udtale
• therefore: udtalen er svær

In Danish, predicative adjectives often agree with the gender/number of the noun:

• en bog er svær = a book is difficult
• et ord er svært = a word is difficult

Since udtale takes en, the adjective is svær.

If the noun were neuter, you would usually get svært instead.

Because fordi introduces a subordinate clause, and in standard Danish subordinate clauses do not use normal main-clause word order.

So you get:

• ..., fordi udtalen er svær

not:

• ..., fordi er udtalen svær

The usual order after fordi is:

• fordi + subject + verb

So:

• fordi udtalen er svær = because the pronunciation is difficult

You may hear different word orders in casual spoken Danish, but the sentence you have is the standard written pattern.

Yes, in standard Danish writing, you normally put a comma before a subordinate clause introduced by fordi.

So:

• Hun staver ordet med ét bogstav ad gangen, fordi udtalen er svær.

That comma marks the start of the explanation clause:

• because the pronunciation is difficult

Yes. Bogstav for bogstav means letter by letter, and it is also very natural Danish.

So a possible alternative is:

• Hun staver ordet bogstav for bogstav, fordi udtalen er svær.

That said, med ét bogstav ad gangen is perfectly correct and emphasizes the idea of doing it one unit at a time.

Mostly yes. At stave means to spell, and it can take a direct object just like in English:

• stave et ord = spell a word
• Hun staver ordet = She spells the word

Danish can also use the verb when someone spells something out loud, which is exactly what is happening in this sentence.