Hun må have bedt viceværten om hjælp, for radiatoren virker igen nu.

Yes. In this sentence, må expresses a logical conclusion, so Hun må have bedt ... means She must have asked ...

It does not mean permission here. Danish må can mean different things depending on context:

• Du må gå nu = You may/can leave now
• Hun må være hjemme = She must be at home
• Hun må have bedt viceværten om hjælp = She must have asked the caretaker for help

So here the speaker is guessing from evidence: the radiator works again, so she probably asked for help.

After a modal verb like må, Danish normally uses the infinitive, not a finite verb form.

So:

• har bedt = has asked
• må have bedt = must have asked

The structure is:

• må
  • have
    • past participle

This is the Danish way to express must have done something.

Compare:

• Hun har bedt viceværten om hjælp = She has asked the caretaker for help
• Hun må have bedt viceværten om hjælp = She must have asked the caretaker for help

Bedt is the past participle of bede (to ask, to request, sometimes to pray in other contexts).

Its main forms are:

• infinitive: bede
• present: beder
• past: bad
• past participle: bedt

So in this sentence, have bedt is the perfect infinitive after må.

Viceværten means the caretaker / the superintendent / the building manager.

The -en ending makes it definite:

• en vicevært = a caretaker
• viceværten = the caretaker

Danish often uses the definite form when the person is understood from the situation. If this is a radiator in an apartment building, there is probably one specific caretaker associated with the building, so viceværten sounds natural.

A vicevært is usually the person who looks after a building or housing complex: repairs, maintenance, practical problems, keys, heating issues, and so on.

Depending on context, English translations might be:

• caretaker
• janitor
• superintendent
• building manager

No single English word matches perfectly in every situation, but caretaker or superintendent is often a good fit here.

Because bede commonly works with this pattern:

• bede nogen om noget = ask someone for something

So:

• Hun bad viceværten om hjælp = She asked the caretaker for help

The person asked comes first, and the thing requested comes after om.

More examples:

• Jeg bad ham om penge = I asked him for money
• Hun bad læreren om råd = She asked the teacher for advice

So om is not optional here; it is part of the normal construction.

Because hjælp is being used as an uncountable noun here, like help in English.

So:

• om hjælp = for help

Just as English usually says ask for help, not ask for a help, Danish says bede om hjælp, not normally bede om en hjælp.

Here for means because or for, introducing an explanation:

• Hun må have bedt viceværten om hjælp, for radiatoren virker igen nu.
• She must have asked the caretaker for help, because the radiator is working again now.

It is not the preposition for meaning for as in a gift for you.

Compared with fordi:

• for often sounds like an explanatory afterthought
• fordi is the more straightforward everyday word for because

So both can often work, but for has a slightly different flavor. In this sentence, it sounds natural because the second clause gives the evidence for the speaker’s conclusion.

Because the sentence has two clauses:

1. Hun må have bedt viceværten om hjælp
2. radiatoren virker igen nu

They are joined by for, and in standard Danish punctuation, a comma is normally written before a conjunction like this when it links two clauses.

So the comma helps show that the second clause explains the first.

That is the normal order with bede in this meaning:

• bede nogen om noget = ask someone for something

So:

• viceværten = the person being asked
• om hjælp = what she asked for

This order is very common and natural in Danish.

Virker means works / is functioning here.

For machines, systems, appliances, and things like radiators, virke is very common in Danish:

• Computeren virker ikke = The computer isn’t working
• Radiatoren virker igen = The radiator is working again

Fungerer is also possible in many contexts, but virker is extremely natural for everyday speech.

Not really. The two adverbs add slightly different information:

• igen = again
• nu = now

So virker igen nu means something like:

• is working again now
• works again now

The idea is that it was not working before, but at the present moment it is working again.

Normally, no. In this kind of sentence, må have + past participle is understood as must have in the sense of deduction.

If you want may have / might have, Danish usually uses something like:

• Hun kan have bedt viceværten om hjælp
• Hun har måske bedt viceværten om hjælp

Those are weaker and more uncertain than Hun må have bedt ...

So:

• må have bedt = fairly strong conclusion: must have asked
• kan have bedt / måske har bedt = weaker possibility: may/might have asked