Þær eru nýbúnar að gróðursetja tvö ný tré við grasflötina.

Þær means they, but specifically for an all-female group.

Icelandic has three third-person plural pronouns:

• þeir = they, for a masculine or mixed group
• þær = they, for a feminine group
• þau = they, for a neuter group, or sometimes for mixed things/non-human groups

So this sentence tells you that the people being referred to are feminine.

Because nýbúnar has to agree with Þær.

The word nýbúinn changes for gender and number, just like an adjective. Here the subject is:

• feminine
• plural

So the correct form is:

• nýbúnar = feminine plural

Compare:

• Hún er nýbúin = she has just finished
• Þeir eru nýbúnir = they (masc./mixed) have just finished
• Þær eru nýbúnar = they (fem.) have just finished

This is a very common Icelandic structure meaning have just done something or have just finished doing something.

So:

• Þær eru nýbúnar að gróðursetja ...
  = they have just planted ... / they have just finished planting ...

Literally, nýbúinn is something like newly finished, so the whole construction expresses a very recent completed action.

This is one of the most natural ways in Icelandic to say have just done something.

Here að is the infinitive marker, similar to English to in to plant.

In the pattern vera nýbúinn að + infinitive, the að is required:

• vera nýbúinn að borða = have just eaten
• vera nýbúinn að koma = have just arrived
• vera nýbúinn að gróðursetja = have just planted

So að gróðursetja means to plant.

Yes, but it would not mean exactly the same thing.

• Þær eru nýbúnar að gróðursetja ...
  = they have just planted / they have just finished planting

• Þær hafa gróðursett ...
  = they have planted ...

The version with nýbúnar að strongly emphasizes that the action happened very recently. The hafa perfect is more neutral and does not automatically include that just now feeling.

Because tré is a neuter noun.

The number two changes by gender in Icelandic:

• tveir for masculine
• tvær for feminine
• tvö for neuter

Since tré is neuter, you get:

• tvö tré = two trees

In this sentence, tvö ný tré is the direct object of the verb.

The adjective has to agree with tré in gender, number, and case.

Here:

• tré is neuter
• it is plural
• it is in the accusative because it is the direct object

The correct strong adjective form for new here is ný.

So:

• tvö ný tré = two new trees

This form may look surprisingly short, but it is the correct neuter plural accusative/nominative form in this phrase.

Not always. Tré is one of those Icelandic neuter nouns whose form is the same in singular and plural in the nominative and accusative.

So:

• tré = a tree
• tré = trees

You can tell singular vs. plural from the rest of the phrase:

• nýtt tré = a new tree
• tvö ný tré = two new trees

Even though the noun itself does not change here, the number word and adjective show that it is plural.

Here við means something like:

• by
• next to
• beside
• at

So við grasflötina means by the lawn or next to the lawn.

It tells you the location of the planting.

The ending -ina is the suffixed definite article, meaning the.

So:

• grasflöt = lawn
• grasflötina = the lawn

Icelandic usually attaches the to the end of the noun instead of putting a separate word before it.

In this sentence, the noun is also in the accusative singular, because við takes the accusative.

Because við normally governs the accusative case.

So after við, you expect an accusative form:

• við grasflötina

This is something learners mostly just have to memorize with prepositions: in Icelandic, prepositions often require a specific case.

Here the important point is:

• við + accusative = by/next to/at

Yes, gróðursetja is one verb, meaning to plant.

It is historically a compound word:

• gróður = vegetation/growth
• setja = set, put

So the verb literally has the sense of set into growth / put into the ground, which matches the idea of planting.

For a learner, the main thing to remember is simply:

• gróðursetja tré = to plant trees