Advarslen på skærmen siger, at filen er for stor til at sende.

The ending -en is the definite article attached to the noun. Danish often says the by adding it to the end of the noun instead of putting a separate word in front.

• en advarsel = a warning

• advarslen = the warning

• en skærm = a screen

• skærmen = the screen

• en fil = a file
• filen = the file

So Advarslen på skærmen means The warning on the screen, and filen means the file.

På usually means on. So på skærmen literally means on the screen.

This is a very natural Danish expression:

• på skærmen = on the screen
• på bordet = on the table
• på væggen = on the wall

So Advarslen på skærmen is simply The warning on the screen.

Here, Advarslen på skærmen is the subject of the sentence, and siger is the verb:

• Advarslen på skærmen = subject
• siger = says

So the structure is straightforward:

• The warning on the screen says ...

You do not need der here because this is not an existential sentence like there is / there are. Danish uses der in sentences such as:

• Der er en fejl = There is an error

But in your sentence, the warning itself is doing the action of saying, so der is not needed.

In standard Danish, a comma is often placed before a subordinate clause introduced by at.

Here:

• Advarslen på skærmen siger = main clause
• at filen er for stor til at sende = subordinate clause

So the comma helps show the boundary between the two parts.

The word at here means that:

• siger, at ... = says that ...

The two at words do different jobs.

1. siger, at filen er for stor ...

   • Here at means that
   • It introduces a clause: says that the file is too large ...

2. for stor til at sende

   • Here at is the infinitive marker, like English to
   • at sende = to send

So:

• first at = that
• second at = to

This is very common in Danish.

Because filen comes from en fil, and fil is a common gender noun in Danish.

Adjectives in Danish agree with the noun in certain contexts:

• en stor fil = a large file
• filen er stor = the file is large

If the noun were a neuter noun (et-word), you would often see stort:

• et stort hus = a big house

So here:

• fil is an en-word
• therefore the adjective is stor

Literally, it means too large to send.

This follows a very common Danish pattern:

• for + adjective + til at + infinitive

Examples:

• for dyr til at købe = too expensive to buy
• for tung til at løfte = too heavy to lift
• for stor til at sende = too large to send

So the structure works much like English too ... to ....

Good question. In English, we also often leave the object unspoken in this pattern:

• The file is too large to send

We understand that send refers to the file, even though it is not repeated.

Danish works the same way here:

• filen er for stor til at sende

The meaning is understood as:

• the file is too large for someone to send
• more naturally: the file is too large to send

You could sometimes make things more explicit in other contexts, but in this sentence it is perfectly normal not to repeat filen as an object.

Because er is the normal present tense of at være = to be, and for stor is the description after it.

So:

• filen er stor = the file is large
• filen er for stor = the file is too large

This is the same basic pattern as English:

• subject + is
  • adjective

Siger is the present tense of at sige = to say.

The sentence describes what the warning says right now:

• Advarslen på skærmen siger ... = The warning on the screen says ...

This is natural because messages, labels, signs, and warnings are often described in the present tense:

• Skiltet siger, at ... = The sign says that ...
• Mailen siger, at ... = The email says that ...

Even in English, we usually do the same.

The basic structure is:

• Advarslen på skærmen = subject
• siger = main verb
• at filen er for stor til at sende = subordinate clause

Inside the subordinate clause, the order is:

• filen = subject
• er = verb
• for stor = complement
• til at sende = infinitive phrase

So the sentence breaks down like this:

• Advarslen på skærmen
• siger
• at filen er for stor til at sende

This is a very normal Danish sentence pattern.

Yes. Danish is a V2 language, which means the finite verb usually comes in the second position in a main clause.

Original:

• Advarslen på skærmen siger, at ...

If you start with På skærmen, then the verb must come right after that fronted element:

• På skærmen siger advarslen, at filen er for stor til at sende.

That sentence is grammatically possible, but it sounds more marked or literary. In ordinary usage, Advarslen på skærmen siger ... is more natural.

Possibly, but the meaning changes slightly.

• advarsel = warning
• meddelelse = message / notice

If the text on the screen is specifically warning the user, advarslen is a good choice.
If you want a more neutral word, meddelelsen could work in some contexts.

So:

• Advarslen på skærmen = the warning on the screen
• Meddelelsen på skærmen = the message on the screen

Both can be correct, depending on what kind of text it is.