Når vi rydder op i haven, kører jeg gammelt græs ud i komposten med trillebøren.

Here når means when or whenever.

In this sentence, it suggests a repeated or typical situation:

• Når vi rydder op i haven = When / Whenever we tidy up in the garden

Why not the others?

• da is usually used for a specific time in the past: when
• hvis means if

So når is the natural choice for something that happens regularly or whenever that situation comes up.

Because Danish main clauses follow the V2 rule: the finite verb must come in the second position.

Here, the whole subordinate clause comes first:

• Når vi rydder op i haven = first element

So the main clause must begin with the verb:

• kører = second position
• jeg = comes after the verb

That gives:

• Når vi rydder op i haven, kører jeg ...

If the sentence started directly with the subject, then you would get normal order:

• Jeg kører gammelt græs ud i komposten med trillebøren, når vi rydder op i haven.

Yes. Rydde op is a fixed verb expression meaning to tidy up or clean up.

So:

• at rydde op = to tidy up
• vi rydder op = we tidy up / are tidying up

The particle op is important. It helps create the meaning of tidy up, not just clear or remove.

In this sentence:

• rydder op i haven means something like tidy up in the garden or, more naturally in English, tidy up the garden.

i haven literally means in the garden.

• i = in
• haven = the garden

Danish often uses rydde op i haven, literally tidy up in the garden, where English might more naturally say tidy up the garden.

So the Danish wording focuses on the location/area where the tidying happens.

Also, haven is the definite form of en have:

• en have = a garden
• haven = the garden

Because græs is being used as a mass noun, like grass, water, or sand in English.

With mass nouns, Danish often uses no article when talking about an unspecified amount:

• gammelt græs = old grass / old cut grass

So this does not mean one specific countable item. It means some amount of old grass, probably grass clippings or dead grass being moved to the compost.

Because græs is a neuter noun in Danish.

Adjectives agree with the noun, and for an indefinite singular neuter noun, the adjective usually gets -t:

• gammel = common gender singular
• gammelt = neuter singular
• gamle = plural or definite

So:

• en gammel stol = an old chair
• et gammelt hus = an old house
• gammelt græs = old grass

Even though græs is often used as a mass noun, the adjective still follows the neuter pattern.

Not necessarily driving in the car sense.

In Danish, at køre can also mean to transport or move something on wheels. That fits very well with a wheelbarrow.

So here:

• kører jeg gammelt græs ud i komposten
  means something like
• I take / wheel / transport old grass out to the compost

Because the sentence later says med trillebøren, the idea is clearly that the speaker is moving the grass with a wheelbarrow.

Because they do slightly different jobs.

• ud = out
• i komposten = into the compost

Together, ud i gives the sense of movement outward and into that destination:

• ud i komposten = out into the compost / out to the compost

This kind of combination is very common in Danish:

• ind i huset = into the house
• ud på gaden = out onto the street
• op i bilen = up into the car

So ud adds direction, while i introduces the place reached.

Because the sentence is talking about a specific, known compost — presumably the one in that garden or at that home.

• en kompost = a compost heap / a compost bin
• komposten = the compost heap / the compost bin

Danish very often uses the definite form when the thing is already identifiable from the situation.

Here, it sounds natural because both speaker and listener can be expected to know which compost is meant.

Both are possible, but they mean slightly different things.

• med trillebøren = with the wheelbarrow, using the wheelbarrow we know about
• med en trillebør = with a wheelbarrow, using some wheelbarrow

The definite form is very natural when talking about an ordinary household object that is understood from context — the wheelbarrow that belongs there or is being used at the time.

So med trillebøren sounds like:

• using the wheelbarrow

rather than introducing a new object.

Because med here expresses the means or tool used to do the action.

• med trillebøren = using the wheelbarrow

If you said i trillebøren, that would focus more on the grass being inside the wheelbarrow:

• græsset ligger i trillebøren = the grass is in the wheelbarrow

So in this sentence, med is better because the wheelbarrow is being presented as the instrument used to move the grass.

Yes.

You can say:

• Jeg kører gammelt græs ud i komposten med trillebøren, når vi rydder op i haven.

That is also correct.

The important difference is word order in the main clause:

• If the sentence starts with the når-clause, you get kører jeg
• If the sentence starts with the subject, you get jeg kører

So the placement of the subordinate clause changes the word order of the main clause, but not the basic meaning.