I dag lærer vi at bruge få sammen med ord som klippet og repareret, når andre gør noget for os.

Yes, få often means get, but in this pattern it has a special use:

få + past participle often means have/get something done by someone else.

So Danish can say things like:

• Jeg får håret klippet. = I’m getting my hair cut / I have my hair cut.
• Vi fik bilen repareret. = We got the car repaired.

In the sentence you gave, the speaker is talking about learning how to use få in exactly that kind of structure.

Because klippet and repareret are past participles, not infinitives.

After få in this construction, Danish normally uses a past participle:

• få håret klippet
• få bilen repareret
• få huset malet

This is different from English, where we often use have/get + object + past participle:

• have my hair cut
• get the car repaired

So klippet and repareret are the right form because they describe the result of the action done to something.

The basic idea is:

subject + få + object + past participle

Examples:

• Jeg får håret klippet.
  = I get my hair cut.

• Hun fik cyklen repareret.
  = She got the bike repaired.

• Vi skal have vinduerne vasket is also common with have, but with få you often see:
  Vi får vinduerne vasket.
  = We get the windows cleaned.

It usually means:

1. someone else performs the action,
2. the subject arranges it, requests it, or causes it to happen.

So it is not usually about doing the action yourself.

Ord som ... means words such as ... or words like ...

So:

• ord som klippet og repareret
  = words such as klippet and repareret

The sentence is explaining a grammar topic, so it refers to these forms as examples of the kind of words used after få.

Because bruge is an infinitive, while klippet and repareret are not.

• at bruge = to use
• klippet = cut / having been cut
• repareret = repaired

So the structure is:

• lærer vi at bruge få = we are learning to use få
• sammen med ord som klippet og repareret = together with words like klippet and repareret

Only the verb bruge needs at here.

Literally it means:

• når = when
• andre = others / other people
• gør noget = do something
• for os = for us

So the whole phrase means:

when other people do something for us

This explains the situation in which the få + participle structure is used: when someone else performs the action on our behalf.

Good question. In Danish:

• når is often used for when in general, repeated, or expected situations
• hvis means if

Here the sentence is describing a general rule:

we use this structure when other people do something for us

So når is the natural choice.

Compare:

• Når jeg får håret klippet, går jeg til frisøren.
  = When I get my hair cut, I go to the hairdresser.
  general/repeated situation

• Hvis jeg får håret klippet i morgen, bliver det kort.
  = If I get my hair cut tomorrow, it will be short.
  conditional/uncertain situation

Because Danish uses verb-second word order in main clauses.

When something other than the subject comes first, the finite verb usually comes next.

So:

• Vi lærer i dag ... = We are learning today ...
• I dag lærer vi ... = Today we are learning ...

The adverbial I dag is moved to the front for emphasis, so the verb lærer must come before the subject vi.

This is very common in Danish.

Here andre means others or other people, and it functions like a pronoun.

So:

• når andre gør noget for os
  = when others do something for us

It does not need a noun after it here. Danish often uses andre this way.

Compare:

• andre mennesker = other people
• andre = others

Not exactly, though the meaning is related.

Compare:

• Bilen bliver repareret.
  = The car is being repaired.
  This is passive. It focuses on the car and the action.

• Jeg får bilen repareret.
  = I get the car repaired.
  This is not just passive. It also suggests that I arrange for it to happen or I have it done.

So få + participle often adds the idea that someone causes or obtains the action, not just that the action happens.

Yes. Få changes tense like a normal verb, while the participle usually stays the same.

Examples:

• Jeg får håret klippet.
  = I get my hair cut. / I’m getting my hair cut.

• Jeg fik håret klippet.
  = I got my hair cut.

• Jeg har fået håret klippet.
  = I have had my hair cut.

• Jeg vil få håret klippet.
  = I will get my hair cut.

So once you learn the pattern, you can use it in many different time frames.

It is talking about a grammar rule in general.

The sentence does not mean that today we are cutting or repairing something. It means:

Today we are learning how to use få with forms like klippet and repareret when someone else does something for us.

So it is classroom/explanatory language about grammar, not a description of an actual event.