Nach dem Arbeitszeugnis frage ich die Personalabteilung.

Because German often uses the pattern jemanden nach etwas fragen for to ask someone about something or to ask someone for something.

So in this sentence:

• die Personalabteilung = the person or department being asked
• nach dem Arbeitszeugnis = the thing being asked about

This is a normal German structure, even though English would usually say ask someone about or ask someone for.

Because nach always takes the dative case.

The noun Arbeitszeugnis is neuter:

• nominative: das Arbeitszeugnis
• dative: dem Arbeitszeugnis

So after nach, you must say dem Arbeitszeugnis.

Because die Personalabteilung is the direct object of fragen.

In the pattern jemanden fragen, the person or institution being asked is in the accusative.

Here, Personalabteilung is feminine:

• nominative: die Personalabteilung
• accusative: die Personalabteilung

So the form stays die. It looks the same as the nominative, but its function is accusative.

The pattern is:

jemanden nach etwas fragen

That means:

• jemanden = someone, in the accusative
• nach etwas = about/for something, with nach
  • dative

So this sentence breaks down as:

• Nach dem Arbeitszeugnis = about the work reference
• frage ich = I ask
• die Personalabteilung = the HR department

German often moves different parts of the sentence into the first position for emphasis or topic.

So both of these are correct:

• Nach dem Arbeitszeugnis frage ich die Personalabteilung.
• Ich frage die Personalabteilung nach dem Arbeitszeugnis.

The second one is probably the more neutral basic order.

The first one puts more attention on Nach dem Arbeitszeugnis. Maybe the speaker wants to stress what they are asking about.

Also notice the normal German rule: the conjugated verb must still be in second position. That is why you get:

• Nach dem Arbeitszeugnis = first position
• frage = second position
• ich = after the verb

Yes. That is completely correct and probably the version many learners would produce first.

It has the same meaning. The difference is mostly word order and emphasis, not basic meaning.

An Arbeitszeugnis is a formal employment reference or work certificate given by an employer.

It is a very important document in German-speaking work culture. It usually summarizes:

• how long someone worked somewhere
• what their role was
• how their performance was evaluated

So it is not just any random certificate. In many contexts, employment reference is the best English understanding.

Not in the usual time sense.

Nach has several meanings in German, including:

• after
• to/toward
• according to
• in fixed expressions like nach etwas fragen

Here it belongs to the verb pattern and means something like about or for.

So you should not read this sentence as if it meant after the work reference, I ask... That is not what is happening here.

Usually no, not with fragen in this structure.

German normally says:

• jemanden nach etwas fragen = ask someone about/for something

If you use über, you would usually need a different verb, for example:

• über etwas sprechen = talk about something

So:

• Ich frage die Personalabteilung nach dem Arbeitszeugnis. = correct
• Ich spreche mit der Personalabteilung über das Arbeitszeugnis. = also correct, but it means I talk with HR about the work reference, not exactly I ask HR for/about it

The article changes the nuance:

• nach dem Arbeitszeugnis = about the work reference, a specific one
• nach einem Arbeitszeugnis = about a work reference, one in general

So dem suggests that the speaker and listener already know which Arbeitszeugnis is meant.

Because German often forms compound nouns.

Personalabteilung is made of:

• Personal = personnel, staff
• Abteilung = department

Together, they mean HR department or personnel department.

In German, the last part usually determines the gender. Since Abteilung is feminine, the whole word is feminine:

• die Abteilung
• die Personalabteilung

Not exactly.

There are two related things here:

• nach etwas fragen = ask about something
• nachfragen = ask again, check again, inquire further

So:

• Ich frage die Personalabteilung nach dem Arbeitszeugnis. = I ask HR about the work reference
• Ich frage bei der Personalabteilung nach. = I check with HR / I follow up with HR

They are related, but they are not identical.

Grammatically, yes, it is present tense. But in German, present tense can cover several English ideas depending on context, such as:

• I am asking
• I ask
• I will ask

So without more context, frage could mean:

• something happening now
• a habitual action
• a near-future plan

German often uses the present tense where English might choose either present or future.