Aan die begin van die maand skryf sy haar afsprake op die kalender neer.

This is a time expression meaning at the beginning of the month. In Afrikaans, it is very common to put a time phrase at the start of the sentence.

Because that first position is occupied by the time phrase, the finite verb must come next:

• Aan die begin van die maand skryf sy ...

This is a standard Afrikaans/V2 word order pattern:

• first element: Aan die begin van die maand
• second element: skryf
• then the subject: sy

If you started with the subject instead, you could also say:

• Sy skryf aan die begin van die maand haar afsprake op die kalender neer.

Afrikaans usually puts the finite verb in second position in a main clause.

So when the sentence begins with a time phrase like Aan die begin van die maand, the verb must come immediately after it:

• Aan die begin van die maand skryf sy ...

This is similar to inversion in some English patterns, but it is much more regular in Afrikaans.

Compare:

• Sy skryf haar afsprake neer.
• Aan die begin van die maand skryf sy haar afsprake neer.

Aan die begin van means at the beginning of.

It is a fixed expression:

• aan = at
• die begin = the beginning
• van = of

So:

• aan die begin van die maand = at the beginning of the month

You can use the same pattern with other nouns:

• aan die begin van die jaar = at the beginning of the year
• aan die begin van die dag = at the beginning of the day

Because Afrikaans often uses the definite article die where English uses the.

Here, the phrase is:

• van die maand = of the month

So the whole expression is literally:

• at the beginning of the month

Without die, the phrase would sound incomplete or unnatural here.

Afsprake is the plural of afspraak.

It usually means:

• appointments
• engagements
• sometimes plans or arrangements, depending on context

In this sentence, haar afsprake most naturally means her appointments.

Examples:

• Ek het 'n afspraak met die dokter. = I have an appointment with the doctor.
• Sy maak haar afsprake vroeg. = She makes her appointments early.

Here, haar means her.

Afrikaans distinguishes:

• sy = she
• haar = her

So in the sentence:

• sy = she
• haar afsprake = her appointments

That means:

• sy skryf haar afsprake neer = she writes down her appointments

It means on the calendar.

In natural English, we might say write her appointments on the calendar. Afrikaans uses the same preposition:

• op die kalender

This tells you where she writes them.

So the structure is:

• skryf = write
• haar afsprake = her appointments
• op die kalender = on the calendar
• neer = down

Together:

• skryf haar afsprake op die kalender neer = writes her appointments down on the calendar

Because neerskryf is a separable verb in Afrikaans.

The full idea is:

• neerskryf = to write down

But in a main clause, the verb often splits:

• the finite part goes earlier: skryf
• the second part goes to the end: neer

So:

• Sy skryf dit neer. = She writes it down.
• Aan die begin van die maand skryf sy haar afsprake op die kalender neer.

This is very common in Afrikaans with separable verbs.

Yes. They are two forms of the same verb.

• neerskryf is the full infinitive form: to write down
• skryf ... neer is the split form used in a main clause

Examples:

• Ek wil dit neerskryf. = I want to write it down.
• Ek skryf dit neer. = I write it down.

So in your sentence, skryf ... neer is just the normal main-clause version of neerskryf.

Yes, but the meaning changes slightly.

• skryf ... neer = write down, emphasizing noting something down
• skryf ... = write, more general

So:

• Sy skryf haar afsprake op die kalender neer. = She writes her appointments down on the calendar.
• Sy skryf haar afsprake op die kalender. = She writes her appointments on the calendar.

The version with neer sounds more complete and more natural if the idea is making a record of them.

There is a word for down: it is neer.

The reason it is not next to skryf is that separable verbs split in Afrikaans main clauses.

English:

• write down

Afrikaans main clause:

• skryf ... neer

Afrikaans infinitive:

• neerskryf

So the meaning is there, but the sentence structure is different.

After the verb and subject, Afrikaans often places:

1. object
2. other information such as place
3. separated verb particle at the end

So here:

• skryf = verb
• sy = subject
• haar afsprake = object
• op die kalender = place/location
• neer = separable particle

That gives:

• Aan die begin van die maand | skryf | sy | haar afsprake | op die kalender | neer

Not very naturally. A very literal version would be:

• At the beginning of the month writes she her appointments on the calendar down.

That shows the Afrikaans structure, but it is not normal English.

A natural English translation would be:

• At the beginning of the month, she writes her appointments down on the calendar. or
• At the beginning of the month, she writes her appointments on the calendar.

So it is better to understand the Afrikaans word order as its own system, not as English with substituted words.

Yes, it is very useful and worth memorizing as a chunk.

You can reuse the pattern easily:

• aan die begin van die week = at the beginning of the week
• aan die begin van die les = at the beginning of the lesson
• aan die begin van die storie = at the beginning of the story

Learning it as one unit will help you produce natural Afrikaans more easily.

Then the separable verb becomes one word again: neerskryf.

For example:

• Sy wil haar afsprake aan die begin van die maand op die kalender neerskryf.
  = She wants to write down her appointments on the calendar at the beginning of the month.

Notice that in this kind of structure, the full infinitive neerskryf stays together at the end.

That is an important contrast:

• main clause: skryf ... neer
• infinitive: neerskryf

A rough English-friendly guide:

• afsprake ≈ AHF-spraa-kuh
• neer ≈ near, but usually with a tenser vowel than in many English accents

A few helpful notes:

• aa in afsprake is a long vowel
• the g in begin and maand is not present, but in many Afrikaans words g is a throaty sound
• ee in neer is long

If you are learning pronunciation, it is best to hear native audio, because Afrikaans vowels are important and do not always match English spelling habits exactly.