Appen er åbenbart nede igen, så jeg kan overhovedet ikke logge ind.

Appen means the app.

In Danish, nouns usually add a suffix to show definiteness:

• en app = an app
• appen = the app

So Appen er ... means The app is ...

Because app is a common-gender noun, the definite ending is -en.

Here åbenbart means something like apparently, evidently, or it seems.

So:

• Appen er åbenbart nede igen = The app is apparently down again

Depending on context, åbenbart can sometimes sound like:

• the speaker has just realized it
• the speaker is drawing an obvious conclusion
• the situation is annoyingly clear

In everyday speech, it often carries a slight feeling of "well, clearly..."

Yes. Nede literally means down or down there, but in tech contexts it works just like English down:

• Serveren er nede = The server is down
• Hjemmesiden er nede = The website is down
• Appen er nede = The app is down

So this is a normal idiomatic use, not a strange metaphor.

Igen means again.

So:

• Appen er åbenbart nede igen = The app is apparently down again

It suggests this has happened before, often with a hint of irritation.

Here så means so.

It connects the two parts:

• Appen er åbenbart nede igen = The app is apparently down again
• så jeg kan overhovedet ikke logge ind = so I absolutely can't log in

So the second part is the consequence of the first.

Because så here is being used like a coordinating conjunction, similar to English so.

That means the clause after it keeps normal main-clause word order:

• så jeg kan ...

Compare:

• Jeg kan ikke logge ind. = I can't log in.
• ..., så jeg kan ikke logge ind. = ..., so I can't log in.

If this were a subordinate clause introduced by a different conjunction, the word order could change. But here så does not trigger subordinate clause word order.

In Danish main clauses, the finite verb usually comes early, and ikke normally comes after that finite verb.

So:

• jeg kan ikke = I cannot / I can't

Not:

• jeg ikke kan in this kind of main clause

That word order changes in subordinate clauses, but in this sentence you have a main clause after så, so kan comes before ikke.

Overhovedet intensifies the negation. It means something like:

• at all
• absolutely
• in any way

So:

• jeg kan ikke logge ind = I can't log in
• jeg kan overhovedet ikke logge ind = I absolutely can't log in / I can't log in at all

It makes the statement stronger and more emphatic.

Because overhovedet typically goes right before ikke when it intensifies the negation.

So the natural order is:

• kan overhovedet ikke logge ind

This is the standard pattern. To an English speaker, it may help to think of overhovedet ikke as a unit meaning not at all.

Logge ind means to log in or to sign in.

It is a very common tech expression in Danish. Like English, Danish often uses borrowed computer-related verbs.

Examples:

• Jeg kan ikke logge ind. = I can't log in.
• Har du prøvet at logge ind igen? = Have you tried logging in again?

Because logge ind works as a verb plus particle, similar to English log in.

In the infinitive after a modal verb, you often see:

• kan logge ind
• vil logge ind
• skal logge ind

So ind stays with the verb phrase, but it appears as a separate word.

This is very similar to English:

• I can log in
• not I can login as a verb phrase

Yes, it sounds slightly frustrated and conversational.

A few things create that tone:

• åbenbart = suggests "apparently / well, clearly"
• igen = suggests it has happened before
• overhovedet ikke = strong emphasis

So the sentence does not just give information. It also sounds like the speaker is annoyed:

• The app is apparently down again, so I absolutely can't log in.

Sometimes yes, but you have to be careful.

Depending on context, åbenbart can mean:

• apparently
• evidently
• obviously

In this sentence, apparently is often the safest translation, because the speaker seems to be concluding from the situation that the app is down. Obviously might sound a bit stronger or more sarcastic in English.

Yes, very natural.

It sounds like something a Danish speaker would say in everyday conversation, especially when talking about a technical problem:

• Appen er åbenbart nede igen, så jeg kan overhovedet ikke logge ind.

It is idiomatic, modern, and completely normal spoken Danish.