Learn Hardcore Icelandic: Dóttirin er núna næstum eins há og móðir hennar. - The daughter is now almost as tall as her mother.

Icelandic has a verb-second (V2) tendency in main statements: the finite verb usually comes in second position, but the first position can be almost anything (subject, adverb, object, etc.).

Here, the subject Dóttirin comes first, and the verb er is second:

Dóttirin (1st slot) er (2nd slot) núna næstum eins há og móðir hennar.

You could start with an adverb instead, for emphasis:

Núna er dóttirin næstum eins há og móðir hennar. – Now the daughter is almost as tall as her mother.

But starting with Er (“Is”) the way you might in a question in English is not grammatical for a normal statement in Icelandic.
Er dóttirin…? would be a question, not a statement.

What is the difference between núna and nú? Could I say Dóttirin er nú næstum eins há…?

Both núna and nú can mean “now”, but they differ slightly in usage and feel:

núna = “now, at this point in time” (neutral, very common in everyday speech)
nú = “now” but also has discourse uses (“well now…”, “so now…”) and can sound a bit more formal or stylistic in some contexts.

In this sentence, both are possible:

Dóttirin er núna næstum eins há og móðir hennar.
Dóttirin er nú næstum eins há og móðir hennar.

The meaning is essentially the same. Núna is a safe, neutral choice for “now” in time expressions like this.

What does the structure eins há og mean?

The pattern eins … og is a very common way to say “as … as” in Icelandic.

eins há og = as tall as
eins gamall og = as old as
eins stór og = as big as

So, without næstum, the core comparison is:

Dóttirin er eins há og móðir hennar.
→ The daughter is as tall as her mother.

In your sentence, næstum modifies this:

næstum eins há og = almost as tall as

What exactly does næstum mean here, and how strong is it?

næstum means “almost, nearly”. It softens the equality expressed by eins … og.

eins há og = as tall as (equally tall)
næstum eins há og = almost as tall as (a little bit shorter)

Other very similar word:

nánast = also “almost, virtually”; often interchangeable with næstum, e.g.
Dóttirin er nánast eins há og móðir hennar.

In everyday speech here, næstum and nánast would usually be understood the same way.

Why is it há and not the dictionary form hár?

The base (dictionary) form of the adjective is hár = tall (masculine nominative singular).
In Icelandic, adjectives agree with the noun in:

gender (masc./fem./neut.)
number (sing./pl.)
case (nom./acc./dat./gen.)

Here the noun is dóttirin:

dóttirin is feminine, singular, nominative (subject)

So hár must take the feminine nominative singular form:

masculine: hár – tall (he is tall) → Hann er hár.
feminine: há – tall (she is tall) → Hún er há.
neuter: hátt – tall/high (it is tall/high) → Það er hátt.

Thus:

Dóttirin er … há – The daughter is … tall (feminine).

Why is it móðir hennar and not móðirin hennar for “her mother”?

In Icelandic, when you have a possessive pronoun (like hennar, hans, mín, etc.), you usually do not also add the definite suffix to the noun.

So:

móðir hennar literally: mother her → understood as “her mother”
(already definite in meaning; you don’t need -in again)

Using móðirin hennar would normally feel redundant or odd in standard language in this context.

This is true for many kinship and body-part nouns:

bróðir minn = my brother (not bróðirinn minn)
faðir hans = his father (not faðirinn hans)

What does hennar mean exactly here, and who does it refer to?

hennar is the 3rd person singular feminine possessive:

hennar = her (belonging to a female person)

In this sentence, the only feminine singular person already mentioned is dóttirin, so hennar naturally refers back to the daughter:

móðir hennar = her mother → the daughter’s mother.

In other contexts, hennar can be ambiguous (“some other woman’s”), and Icelandic has a reflexive possessive (sinn/sín/sitt) to make “one’s own X” clearer, but that’s a more advanced topic. Here, in a simple sentence about a daughter and her mother, it’s understood as her own mother.

Why is it móðir and not some other form like móður?

Icelandic nouns change form (decline) according to case, number, etc. Móðir (“mother”) is a feminine noun with an irregular stem, and it looks different in different cases:

Nominative singular: móðir – the mother (as subject)
Accusative singular: móður – I saw (my) mother → Ég sá móður mína.
Dative singular: móður – I gave to (my) mother
Genitive singular: móður – of (my) mother

In your sentence, móðir hennar is in the nominative, because it is the thing being compared to (like another “subject” of being tall in the comparison):

…eins há og móðir hennar (er).
→ …as tall as her mother (is).

So we use the nominative form móðir.

Why is there no “is” after móðir hennar, like in English “as tall as her mother is”?

In Icelandic, after comparisons like eins … og, the verb “er” (is) is often left out if it would just repeat what is already clear.

The full, explicit version would be:

Dóttirin er núna næstum eins há og móðir hennar er.
= The daughter is now almost as tall as her mother is.

But it is completely normal and more natural to drop the second er:

Dóttirin er núna næstum eins há og móðir hennar.

Speakers automatically understand the implied er at the end.

Could I say the same thing without næstum? How would the meaning change?

Yes:

Dóttirin er núna eins há og móðir hennar.

This would mean:

The daughter is now *as tall as her mother.*
→ implying they are (approximately) the same height.

With næstum:

Dóttirin er núna næstum eins há og móðir hennar.
→ The daughter is now *almost as tall as her mother.*
→ she’s still a bit shorter.

How would the sentence change if it were a son instead of a daughter?

You would change the subject noun and the adjective agreement, and probably also the possessive pronoun (since sonur is masculine):

Sonurinn er núna næstum eins hár og móðir hans.
→ The son is now almost as tall as his mother.

Changes:

dóttirin (fem.) → sonurinn (masc.)
há (fem. form of hár) → hár (masc. form)
hennar (her) → hans (his), now referring to a male person.

Where can núna and næstum go in the sentence? Is the word order fixed?

Icelandic word order is somewhat flexible for adverbs, although there are preferred positions. The original:

Dóttirin er núna næstum eins há og móðir hennar.

Other natural possibilities:

Dóttirin er næstum núna eins há og móðir hennar. (less common; slightly marked)
Núna er dóttirin næstum eins há og móðir hennar. (emphasizes “now”)
Dóttirin er núna eins há næstum og móðir hennar. (odd; usually not used)

The most natural and common version is exactly what you have:

time adverb (núna) before degree adverb (næstum) before eins … og.

So while some movement is possible, “er núna næstum eins há og…” is the idiomatic pattern here.