Forresten kommer der også en notifikation i appen, og desuden sender skolen en påmindelse.

Forresten means something like by the way or incidentally.

It is often used to add an extra piece of information that was not the main point, for example:

• Forresten, jeg så Anna i går. = By the way, I saw Anna yesterday.

In your sentence, it signals that the speaker is adding another detail.

This is because Danish main clauses follow the V2 rule: the finite verb usually comes in second position.

Here, Forresten is placed first. That means the verb must come next:

• Forresten
  • kommer
    • ...

So:

• Forresten kommer der også en notifikation i appen.

Not:

• Forresten der kommer også en notifikation...

This is very common in Danish. If you move something to the front, the verb still stays second.

Here, der is not the locational word there. It is a grammatical dummy subject, similar to English there in sentences like:

• There comes a message
• There is a problem

The clause is introducing something new and indefinite:

• en notifikation

So der helps build that kind of sentence:

• Der kommer en notifikation. = A notification comes / There comes a notification

After Forresten is moved to the front, the order becomes:

• Forresten kommer der også en notifikation

So der is part of the sentence structure, not a place word.

They all add information, but they do not mean exactly the same thing.

• forresten = by the way / incidentally
  • adds an extra remark
• også = also / too
  • simply says something is added
• desuden = moreover / besides / in addition
  • sounds a bit more formal or deliberate than også

In your sentence:

• Forresten introduces an extra point
• også says that a notification is added as well
• desuden adds another supporting detail: the school also sends a reminder

So the sentence stacks several kinds of addition.

Også usually goes before the part it logically adds emphasis to, but in main clauses it often appears in the sentence adverb position, after the finite verb and after a dummy subject like der.

So this is natural:

• Der kommer også en notifikation i appen.

After fronting Forresten:

• Forresten kommer der også en notifikation i appen.

Here også means that this notification is one more thing that happens.

In this sentence, i appen is the natural choice because the notification appears inside the app.

• i appen = in the app

Danish often uses i for something contained within an app, system, document, or interface.

You may sometimes hear på with digital platforms, especially websites or services, but with a notification appearing within an app, i appen is very idiomatic.

Because Danish usually adds the definite article as an ending.

• en app = an app
• appen = the app

So i appen means in the app.

This works the same way with many nouns:

• en bil = a car
• bilen = the car

The sentence uses appen because it refers to a specific app already known from the context.

Because both notifikation and påmindelse are common-gender nouns in Danish, so they take en in the indefinite singular.

• en notifikation
• en påmindelse

This is something you usually just have to learn with each noun: whether it takes en or et.

Because the two clauses are built differently.

In the first clause, the sentence introduces something new in a presentational way:

• der kommer ... en notifikation

That kind of structure often uses dummy der.

In the second clause, the subject is a definite, known thing:

• skolen = the school

So Danish uses a normal main-clause pattern:

• desuden
  • sender
    • skolen
      • en påmindelse

Again, because of the V2 rule, when desuden is placed first, the verb comes second:

• Desuden sender skolen en påmindelse.

They are related, but not identical.

• notifikation = notification
  • a general alert or message from an app or system
• påmindelse = reminder
  • something specifically meant to remind you of something

So a notifikation is a broad technical term, while a påmindelse usually has the function of reminding.

In this sentence, the app gives a notification, and the school sends a reminder.

Yes.

• kommer = present tense of komme
• sender = present tense of sende

Danish often uses the present tense for things happening now, regularly, or as part of a system or scheduled process. So the sentence can describe what normally happens:

• a notification comes in the app
• the school sends a reminder

That is very natural in Danish.