Der Netzbetreiber bucht die Anschlussgebühr ab.

Because the verb here is abbuchen, which is a separable verb.

In a normal main clause, German splits many separable verbs:

• Der Netzbetreiber bucht die Anschlussgebühr ab.

The bucht part goes in the usual verb position, and the prefix ab moves to the end.

Compare:

• infinitive: abbuchen
• main clause: Er bucht die Gebühr ab.
• subordinate clause: ..., weil er die Gebühr abbucht.

So the ab at the end is completely normal.

Abbuchen is often used in financial contexts and usually means something like:

• to debit
• to deduct
• to charge to an account

It is more specific than plain buchen.

• buchen can mean to book, to reserve, or to enter/post something in an accounting sense.
• abbuchen adds the idea of money being taken away from an account.

So in this sentence, the company is not just recording the fee; it is actually debiting it.

They show the gender and case of the nouns.

• der Netzbetreiber = masculine singular, nominative
  This is the subject, the one doing the action.

• die Anschlussgebühr = feminine singular, accusative
  This is the direct object, the thing being debited.

So the structure is:

• Der Netzbetreiber = the network operator
• bucht ... ab = debits
• die Anschlussgebühr = the connection fee

A useful detail: for feminine nouns, die is the same in both nominative and accusative singular, so the form does not change here.

You can tell from both meaning and case/article form.

In this sentence:

• Der Netzbetreiber is in the nominative, so it is the subject
• die Anschlussgebühr is the accusative object

English learners often rely mostly on word order, and that works here too:

• subject first
• verb second
• object after that

So this is a straightforward sentence:

• The network operator debits the connection fee

It is a compound noun, which German uses very often.

• Anschluss = connection, hookup, access, line
• Gebühr = fee, charge

So Anschlussgebühr is literally something like connection fee.

The important grammar point is that the last part of a German compound decides the gender:

• die Gebühr is feminine
• therefore die Anschlussgebühr is also feminine

That is why the sentence uses die Anschlussgebühr.

It is another German compound noun:

• Netz = network
• Betreiber = operator

So Netzbetreiber means network operator.

Again, the last part determines the gender:

• der Betreiber is masculine
• therefore der Netzbetreiber is also masculine

Yes, German often leaves that unstated if it is clear from context.

A fuller version could be:

• Der Netzbetreiber bucht die Anschlussgebühr von meinem Konto ab.

That means:

• The network operator debits the connection fee from my account.

In the shorter sentence, the account is simply not mentioned because abbuchen already strongly suggests money being taken from an account.

No, not in a normal main clause.

Because abbuchen is separable, standard main-clause word order is:

• Der Netzbetreiber bucht die Anschlussgebühr ab.

Not:

• Der Netzbetreiber abbucht die Anschlussgebühr.

But abbucht does appear as one word in other structures, especially when the verb goes to the end:

• ..., weil der Netzbetreiber die Anschlussgebühr abbucht.

So:

• main clause → split: bucht ... ab
• subordinate clause → together: abbucht

Here are some common forms of abbuchen:

• infinitive: abbuchen
• present: er bucht ab
• simple past: er buchte ab
• perfect: er hat abgebucht

Examples:

• Der Netzbetreiber bucht die Anschlussgebühr ab.
• Der Netzbetreiber buchte die Anschlussgebühr ab.
• Der Netzbetreiber hat die Anschlussgebühr abgebucht.

Notice that in the perfect tense, the past participle is abgebucht.

It could be either, depending on context.

German present tense can describe:

• a current action
• a regular/habitual action
• sometimes a scheduled future action

So this sentence could mean:

• the operator is debiting the fee now
• the operator usually debits this fee
• the operator will debit this fee as part of the normal process

You need context to know which is meant.

Sometimes yes, depending on context.

• debits is the more literal translation of abbucht
• charges may sound more natural in some English contexts

But there is a nuance:

• charges a fee focuses on imposing the fee
• debits the fee focuses on taking the money from an account

So abbuchen is closer to debit or deduct from an account than to the broader verb charge.