I dag lærer vi udtrykkene “hvem som helst”, “hvad som helst”, “hvor som helst” og “når som helst”, som vi bruger, når vi ikke vil være præcise.

Yes, standard Danish writes it as i dag, two words.

It is only capitalized here because it starts the sentence. In the middle of a sentence, you would normally write:

• Vi lærer det i dag.

So for a learner, the important point is:

• i dag = normal spelling
• I dag = same phrase, just capitalized at the beginning of a sentence

Udtrykkene is the definite plural form of udtryk.

This noun changes like this:

• et udtryk = an expression
• udtrykket = the expression
• udtryk = expressions
• udtrykkene = the expressions

So in the sentence, udtrykkene means the expressions, because the speaker is talking about specific expressions that are about to be listed.

Here it means learn.

The verb at lære can correspond to both to learn and to teach, depending on context, which can be confusing for English speakers.

Compare:

• Vi lærer udtrykkene. = We are learning the expressions.
• Vi lærer jer udtrykkene. = We teach you the expressions.

So the object structure helps you understand the meaning.

Also note that lærer can be a noun:

• en lærer = a teacher

These are very common Danish patterns built from a question word + som helst.

They mean that the person, thing, place, or time is not specific.

The four in your sentence are:

• hvem som helst = anybody / anyone
• hvad som helst = anything
• hvor som helst = anywhere
• når som helst = anytime / whenever

This is why the sentence says they are used når vi ikke vil være præcise — when we do not want to be precise.

A useful way to think about them is:

• hvem = who
• hvad = what
• hvor = where
• når = when

and then som helst makes them vague or unrestricted.

Not very well. It is best to treat som helst as a fixed idiomatic piece.

Even though helst by itself often means something like preferably / rather / ideally, that is not how you should understand it inside expressions like:

• hvem som helst
• hvad som helst
• hvor som helst
• når som helst

In these, som helst functions as part of a fixed pattern meaning roughly any ... at all or ...soever.

So for learners, the safest approach is:

• learn the whole expression as one unit
• do not try to build the meaning word-for-word

No. The pattern is broader.

You can also use som helst with forms of hvilken:

• en hvilken som helst bog = any book whatsoever
• hvilket som helst svar = any answer whatsoever
• hvilke som helst mennesker = any people whatsoever

So the pattern is not limited to the four examples in the sentence. But hvem/hvad/hvor/når som helst are among the most common and useful ones.

No, it is doing a different job there.

In:

• hvem som helst
• hvad som helst
• etc.

som helst is part of a fixed expression.

But in:

• udtrykkene, som vi bruger ...

the word som is a relative pronoun, meaning something like that / which in English.

So:

• udtrykkene, som vi bruger = the expressions that we use

This is a very common Danish use of som.

So even though the word looks the same, the function is different:

• som in som helst = part of an idiomatic pattern
• som in som vi bruger = relative pronoun

Because når vi ikke vil være præcise is a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, you would usually say:

• Vi vil ikke være præcise.

But after a subordinating word like når, the negation ikke comes before the finite verb:

• når vi ikke vil være præcise

This is a very important Danish pattern.

A simple contrast:

• Vi kommer ikke i dag. = main clause
• fordi vi ikke kommer i dag = subordinate clause

So in your sentence, the placement of ikke is normal subordinate-clause word order.

Because the adjective agrees with the subject vi.

Here, præcise is a predicate adjective after være, and with a plural subject like vi, Danish normally uses the -e form:

• Jeg vil være præcis. = I want to be precise.
• Vi vil være præcise. = We want to be precise.

So:

• singular subject → often præcis
• plural subject → præcise

That is why the sentence has vi ... være præcise.

Yes, it is the same basic word, but it has different functions in the two places.

In:

• når som helst

it is part of a fixed expression meaning any time / whenever / anytime at all.

In:

• når vi ikke vil være præcise

it is a conjunction meaning when.

So the base idea is still about time, but the grammar is different.

You can think of it like English when:

• When we arrive, ... → conjunction
• any time / whenever → more indefinite time reference

Not exactly.

• hvem som helst = anyone / anybody at all
• alle = everyone / all people

This difference is important.

For example:

• Hvem som helst kan lave den fejl. = Anyone can make that mistake.
  This means the mistake is possible for any person; it does not mean that everyone actually makes it.

• Alle laver den fejl. = Everyone makes that mistake.
  This means all people do it.

So hvem som helst is about no restriction on who, while alle is about the whole group.

A few helpful pronunciation notes:

• hvem: the h is silent, so it sounds roughly like vem
• hvad: the h is also silent; in careful speech it is roughly vad, and in everyday speech it can be reduced further
• helst: this is often quite compressed in real speech, so listen to native audio if possible

For an English speaker, the main thing is:

• do not pronounce the initial h in hvem and hvad

That will already make your pronunciation much more natural.