Ég sker peru smátt og set hana í hafragrautinn.

Skera is the dictionary form, meaning to cut.
In the sentence, the verb has to match ég (I), so it becomes the 1st person singular present tense:

• að skera = to cut
• ég sker = I cut
• þú skerð = you cut
• hann/hún sker = he/she cuts

So ég sker is the normal finite verb form here.

Because pera is the direct object of sker, and Icelandic marks direct objects with case.

The noun is:

• nominative: pera
• accusative: peru

Since the sentence says I cut a pear, pear is the thing being cut, so Icelandic uses the accusative: peru.

Hana means her/it in the accusative feminine singular, and it refers back to peru.

That happens because:

1. pera is a feminine noun in Icelandic.
2. The pronoun is the object of set (put), so it must be in the accusative.

So:

• hún = she / it
• hana = her / it

Even though a pear is not female in real life, Icelandic grammar still treats pera as feminine, and the pronoun must match that grammatical gender.

Because Icelandic pronouns usually follow grammatical gender, not natural gender.

Since pera is feminine, the matching pronoun is feminine too:

• pera → hana

If the noun were neuter, then það might be used. So this is not about whether the pear is biologically female; it is purely grammatical.

Here smátt means something like finely, small, or into small pieces.

Literally, it comes from an adjective meaning small, but Icelandic often uses the neuter singular form of an adjective adverbially. So smátt can describe how the cutting is done.

So sker peru smátt means:

• cut the pear finely
• cut the pear into small pieces

Because Icelandic often uses the neuter singular form of an adjective as an adverb-like form.

So even though pera is feminine, smátt is not agreeing with pera here as a normal adjective. Instead, it is functioning adverbially, describing the action sker.

Compare the idea in English:

• a small pear → adjective modifying a noun
• cut small / cut finely → word describing the action

That is what smátt is doing here.

Because the subject is still the same: I.

In coordinated clauses with og (and), Icelandic often leaves out the repeated subject if it is obvious:

• Ég sker peru smátt og set hana í hafragrautinn.

This works just like English:

• I cut a pear finely and put it in the oatmeal.

You could repeat ég, but it is usually unnecessary unless you want emphasis.

Hafragrautur is the basic dictionary form, meaning oatmeal / porridge.

In the sentence, it appears as hafragrautinn, which includes two things:

1. accusative singular
2. the suffixed definite article -inn = the

So:

• hafragrautur = oatmeal / porridge
• hafragrautinn = the oatmeal / the porridge

Icelandic usually attaches the to the end of the noun instead of using a separate word.

Because í can take different cases depending on meaning:

• accusative = motion into
• dative = location in

Here, the pear is being moved into the oatmeal, so Icelandic uses the accusative:

• í hafragrautinn = into the oatmeal

If you were describing something already located there, you would use the dative instead:

• í hafragrautnum = in the oatmeal

This is a very important Icelandic pattern with prepositions.

It is the usual Icelandic word for oatmeal or porridge made from oats.

Depending on context, English might translate it as:

• oatmeal
• porridge
• oatmeal porridge

So the exact English wording can vary, but the Icelandic word refers to that oat-based dish.

Because the most natural order here is:

• verb
• object
• adverbial element

So:

• sker = cuts
• peru = a pear
• smátt = finely / into small pieces

That gives sker peru smátt.

Icelandic word order is somewhat flexible, but this version sounds natural and straightforward. Putting smátt before peru would usually sound less natural in this sentence.

Yes, if the pear has already been mentioned or is clear from context.

For example:

• Ég tek peru. Ég sker hana smátt.
  I take a pear. I cut it finely.

In your sentence, the speaker first introduces the noun peru and then refers back to it with hana in the second part. That is a very natural Icelandic pattern.

It can be either, depending on context.

Icelandic present tense often works like English present tense:

• it can describe something happening now
• it can describe a habitual action
• it can even sound like a recipe or instruction style in the right context

So Ég sker peru smátt og set hana í hafragrautinn could mean:

• something I am doing right now
• something I usually do
• a step in how I prepare my food

The surrounding context tells you which one is meant.