Ég skrifa stutta athugasemd með tvípunkti: „Athugaðu þessa aðalsetningu,“ og set svo aukasetninguna í sviga.

Because athugasemd is the direct object of skrifa, so it is in the accusative case.

• dictionary form: stutt athugasemd
• accusative singular feminine: stutta athugasemd

The adjective stuttur has to agree with the noun in gender, number, and case, so it changes to stutta.

Because með normally takes the dative case in Icelandic.

So:

• nominative: tvípunktur
• dative: tvípunkti

That is why the sentence says með tvípunkti.

Athugaðu is the singular imperative of að athuga.

It means a command directed at one person, like check or notice in English. The ending -ðu is very common in Icelandic imperatives of this type, compare forms like talaðu from að tala.

Because both words are in the accusative feminine singular.

• þessi changes by case, gender, and number
• accusative feminine singular of þessi is þessa
• aðalsetning in the accusative singular is aðalsetningu

So þessa aðalsetningu means this main clause as the object of Athugaðu.

These are grammar terms.

• aðalsetning = main clause / independent clause
• aukasetning = subordinate clause / dependent clause

A learner may notice that Icelandic uses these terms very straightforwardly: aðal- means main, and auka- here means added or subordinate.

That ending shows the definite article, which in Icelandic is usually attached to the end of the noun.

So:

• aukasetning = subordinate clause
• aukasetningu = subordinate clause, accusative singular
• aukasetninguna = the subordinate clause, accusative singular

It is accusative here because it is the object of set.

Because Icelandic, like English, can leave out the subject in the second part of a coordinated sentence when it is the same as before.

So:

• Ég skrifa ... og set svo ...

works like English:

• I write ... and then put ...

The subject ég is understood from the first clause.

Here svo means something like then, after that, or next.

It connects the two actions:

1. Ég skrifa stutta athugasemd ...
2. og set svo aukasetninguna í sviga

So it helps show sequence.

Icelandic normally uses the expression í sviga for in parentheses / in brackets.

Even though English often uses a plural word, Icelandic commonly uses this singular form idiomatically. Also, with í, Icelandic can use accusative or dative depending on meaning, but with svigi the singular form sviga looks the same in both accusative and dative, so the form itself does not show the difference clearly here.

Yes. The quotation marks „ ... “ are a standard Icelandic style, especially in more careful writing and print.

The colon before the quotation is also normal when introducing exact words or an example. In digital writing, you may also see other quotation styles, but „ ... “ is very recognizable as Icelandic usage.