Hún saxar selleríið hægt, en ég sker hvítkálið hraðar.

They are related, but not identical.

• saxa usually means to chop/mince into small pieces
• skera means to cut/slice

So:

• Hún saxar selleríið hægt = she is chopping the celery slowly
• ég sker hvítkálið hraðar = I cut/slice the cabbage faster

Icelandic often makes this distinction more clearly than English does.

That -ið is the definite article attached to the end of the noun.

In Icelandic, the is very often added as a suffix instead of written as a separate word.

• sellerí = celery

• selleríið = the celery

• hvítkál = white cabbage
• hvítkálið = the white cabbage

Both of these nouns are neuter singular, and -ið is the normal definite ending for that form.

Because the noun already ends in -í, and then the definite ending -ið is added.

So:

• sellerí
  • -ið → selleríið

Nothing strange is happening grammatically; it just looks unusual in writing because the noun ends in a vowel and the article also begins with one.

They are direct objects, so they are in the accusative case.

• Hún saxar selleríið
• ég sker hvítkálið

Both verbs, saxa and skera, normally take an accusative object.

In this sentence, you do not see a special accusative ending difference, because many neuter singular nouns look the same in the nominative and accusative.

Yes, historically it is an adjective form, but Icelandic often uses the neuter singular of an adjective adverbially.

So:

• hægur = slow
• hægt = slowly / in a slow way

This is very common in Icelandic. A learner coming from English often expects a special -ly type ending, but Icelandic often does not work that way.

Yes. hraðar here is an adverb in the comparative, meaning more quickly or faster.

You can think of it like this:

• hratt = fast / quickly
• hraðar = faster / more quickly

So:

• hægt = slowly
• hraðar = faster

Notice that the sentence switches roots, just like English often does:

• slowly ... faster

rather than something like slowly ... more slowly.

Because en means but, and it does not by itself force inversion.

The second clause starts with the subject ég, so the normal order is:

• ég sker hvítkálið hraðar

This also fits Icelandic’s usual verb-second pattern:

• first element: ég
• second element: sker

If you started the clause with another element, then inversion would happen:

• en hraðar sker ég hvítkálið

That is possible, but it is more marked in style.

Yes, both are neuter.

That matters because it affects forms like the definite ending:

• selleríið
• hvítkálið

The most reliable way to know noun gender is to learn it together with the noun, usually from a dictionary. Icelandic dictionaries often mark gender like this:

• sellerí (hk.)
• hvítkál (hk.)

Here hk. means hvorugkyn, which is neuter gender.

Yes, but the meaning would change slightly.

• selleríið / hvítkálið = the celery / the cabbage
• sellerí / hvítkál = celery / cabbage in a more indefinite or generic sense

So if you are talking about specific vegetables already known in the situation, the definite forms in the sentence are natural.

saxar is fairly regular, but sker comes from a more irregular verb.

• saxa → hún saxar
• skera → ég sker

With skera, the stem changes, so it is worth memorizing separately. Some common forms are:

• infinitive: skera
• present: ég sker
• past: skar
• past participle: skorið

So a learner should especially remember that ég sker comes from skera.