Hun skriver tidspunktet i sin kalender, så hun ikke glemmer det.

Because it refers to a specific time that’s already known in context (the time she just found out / agreed on). Danish often uses the definite form for something specific: et tidspunkt (a time point) → tidspunktet (the time point / the time).

Here så means so that / in order that and introduces a purpose clause: she writes it down so that she won’t forget it.
The comma is standard Danish punctuation when a main clause is followed by a subordinate clause:
Hun skriver ..., så hun ikke glemmer ...

Because så introduces a subordinate clause. In Danish subordinate clauses, sentence adverbs like ikke typically come before the finite verb:

• Subordinate: ... så hun ikke glemmer det
• Main clause (V2 word order): Hun glemmer det ikke

Sin/sit/sine is the reflexive possessive, used when the owner is the subject of the clause. Since hun is the subject and it’s her own calendar, Danish prefers sin kalender.
Hendes kalender is non-reflexive and often implies contrast or that it’s someone else’s from another perspective (or just adds emphasis).

They agree with the noun being possessed:

• sin
  • common gender singular (en-words): sin kalender
• sit
  • neuter singular (et-words): sit hus
• sine
  • plural: sine bøger

You typically put things in a calendar (as an entry): i kalenderen / i sin kalender.
på is used more for surfaces or platforms (e.g., på væggen, på nettet). You might hear på kalenderen in some contexts, but i kalenderen is the most standard for writing/entering an appointment.

Det refers back to tidspunktet (the time).
Also note the agreement: tidspunkt is neuter (et tidspunkt), so the pronoun is det (not den).

It’s correct and natural. Depending on context, Danes also commonly say:

• Hun skriver det i sin kalender (using det instead of repeating tidspunktet)
• Hun noterer tidspunktet i sin kalender (a bit more like “notes down”)
• Hun skriver tidspunktet ned (writes it down)

It’s present tense: skriver, glemmer. Danish doesn’t have a mandatory progressive like is writing. Present tense can cover both habitual and “right now” meanings depending on context.

A few common learner trouble spots:

• skriver: the -er ending is usually a weak, unstressed sound.
• tidspunktet: stress is on the first part (TID-), and the final -et is also weak/unstressed.
• ikke: often reduced in fast speech (the vowels can sound less clear), but it still sits before the verb in the subordinate clause: hun ikke glemmer.