Receptionisten var meget professionel, selv da systemet gik ned.

Because Receptionisten means the receptionist.

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

• en receptionist = a receptionist
• receptionisten = the receptionist

So this is the definite form of the noun.

For the same reason: systemet means the system.

Danish often forms the definite noun by adding an ending:

• et system = a system
• systemet = the system

The ending depends on the gender of the noun:

• common gender nouns often take -en
• neuter nouns often take -et

So:

• receptionist is common gender → receptionisten
• system is neuter → systemet

Var is the past tense of at være (to be).

• er = is / are
• var = was / were

Since the sentence describes a past situation, Danish uses var:

• Receptionisten er meget professionel = The receptionist is very professional
• Receptionisten var meget professionel = The receptionist was very professional

Meget here means very, and it modifies the adjective professionel.

So:

• meget = very
• professionel = professional

Together:

• meget professionel = very professional

A useful point: meget can mean different things depending on context:

• before an adjective/adverb: very
• Han arbejder meget = He works a lot
• meget vand = much / a lot of water

Because the adjective agrees with Receptionisten, which is a singular common-gender noun.

Adjective forms often work like this:

• common gender singular: professionel
• neuter singular: professionelt
• plural / definite: professionelle

So:

• Receptionisten var professionel = correct
• Systemet var professionelt = correct, because systemet is neuter

In your sentence, the person being described is receptionisten, so professionel is the right form.

Selv da means even when here.

Breaking it down:

• selv = even
• da = when

So:

• selv da systemet gik ned = even when the system went down / crashed

This adds a sense of contrast: the receptionist stayed professional despite the problem.

Because da is normally used for a specific event in the past.

A common rule is:

• da = when for a single completed past event
• når = when for something habitual, repeated, or future-related

So in your sentence:

• selv da systemet gik ned = even when the system went down

This refers to a specific past incident, so da is the natural choice.

Compare:

• Da systemet gik ned, blev alle stressede. = When the system went down, everyone got stressed.
• Når systemet går ned, bliver alle stressede. = When the system goes down, everyone gets stressed.

Here gik ned means went down, stopped working, or crashed.

It comes from the verb at gå ned, which can have several meanings depending on context. With computers, networks, and systems, it often means:

• to go down
• to fail
• to crash
• to stop working

So systemet gik ned is a very natural way to say:

• the system went down
• the system crashed

It is not about physically moving downward here.

Yes, very often it works like a set expression, especially with technology.

Examples:

• Internettet gik ned. = The internet went down.
• Serveren gik ned. = The server went down.
• Systemet gik ned. = The system went down.

Danish uses many verb + particle combinations like this, and their meaning is not always literal.

Because that part is a subordinate clause.

The main clause is:

• Receptionisten var meget professionel

The subordinate clause is:

• selv da systemet gik ned

In standard Danish writing, subordinate clauses are commonly separated with a comma. So the comma helps show the structure of the sentence.

The structure is:

• Receptionisten = subject
• var = verb
• meget professionel = subject complement
• selv da systemet gik ned = subordinate clause

So the full pattern is roughly:

subject + verb + complement + subordinate clause

That makes the main message:

• The receptionist was very professional

And then the subordinate clause adds the circumstance:

• even when the system went down

Not in this sentence.

Professionelt would be wrong here because it does not match receptionisten. You are describing the receptionist, so you need the adjective form that agrees with that noun:

• Receptionisten var meget professionel. = correct

But professionelt can be correct in other contexts, for example with a neuter noun or sometimes adverb-like use:

• Det var meget professionelt. = That was very professional.

Here det is treated as neuter, so professionelt is correct.

Yes. Selv often means even or self, depending on context.

In this sentence, it means even:

• selv da systemet gik ned = even when the system went down

Other examples:

• Selv børnene forstod det. = Even the children understood it.
• Hun gjorde det selv. = She did it herself.

So the exact meaning of selv depends on how it is used in the sentence.