Jeg sendte ved en fejl beskeden til min chef.

Sendte is the simple past of at sende (to send).

• jeg sender = I send / I am sending
• jeg sendte = I sent
• jeg har sendt = I have sent

In this sentence, sendte simply tells you the action happened in the past. Danish often uses the simple past where English might also use have sent, depending on context.

Yes, ved en fejl is a very common fixed expression meaning by mistake or accidentally.

Literally, it is something like by an error, but you should learn it as a whole phrase:

• ved en fejl = by mistake
• ikke med vilje = not on purpose

So in this sentence, it explains how the message was sent: it happened accidentally.

Because beskeden is the definite form: the message.

In Danish, the definite article is usually added to the end of the noun:

• en besked = a message
• beskeden = the message

So the sentence refers to a specific message, not just any message.

Besked usually means message in a broad sense. It can be:

• a written message
• a spoken message
• a text/chat message, depending on context

If you want to be very specific about an SMS, Danish often uses sms or sms-besked. But besked is perfectly natural when the context already makes it clear.

Yes, it can go somewhere else. Danish is fairly flexible with adverbial phrases like ved en fejl.

These are all possible, though the nuance or emphasis may shift a little:

• Jeg sendte ved en fejl beskeden til min chef.
• Jeg sendte beskeden til min chef ved en fejl.
• Ved en fejl sendte jeg beskeden til min chef.

The version you were given is completely natural. Putting ved en fejl earlier can make the mistake feel slightly more central.

Because til is the normal preposition for the recipient/destination of something being sent.

• sende noget til nogen = send something to someone

So:

• Jeg sendte beskeden til min chef = I sent the message to my boss

This is the standard pattern with sende.

Yes, you can. That structure is also possible.

• Jeg sendte beskeden til min chef
• Jeg sendte min chef beskeden

Both mean roughly I sent my boss the message.

The version with til is often clearer and very common, especially for learners. The double-object version (min chef beskeden) is also natural, but may feel slightly more like English I sent my boss the message.

Because in Danish, a possessive like min (my) normally replaces the article.

So you say:

• min chef = my boss
• not den min chef

This is similar to English: we say my boss, not the my boss.

No. In Danish, chef means boss, manager, or person in charge.

So:

• min chef = my boss

It does not normally mean a cook or professional kitchen chef the way English often uses chef.

Danish nouns have grammatical gender, and fejl is a common-gender noun, so it takes en:

• en fejl = a mistake
• fejlen = the mistake

Unfortunately, gender often has to be learned noun by noun.

Because Danish follows the V2 rule in main clauses: the finite verb normally comes in the second position.

So:

• Jeg sendte ved en fejl beskeden til min chef.
• Ved en fejl sendte jeg beskeden til min chef.

When Ved en fejl moves to the front, sendte still has to stay in second position, so jeg moves after the verb.

This is a very important Danish word-order pattern.

Yes. A very common alternative is:

• Jeg kom til at sende beskeden til min chef.

This also means I accidentally sent the message to my boss.

The expression komme til at + infinitive is extremely common for accidental actions:

• Jeg kom til at glemme det = I accidentally forgot it
• Jeg kom til at sige det = I accidentally said it

So your original sentence is correct, but this alternative is also very natural.