Ég skrifa fundinn í dagatalið mitt og set líka áminningu í símann.

Because fundinn is the accusative definite singular form of fundur.

Here, fundinn is the direct object of skrifa, so it goes into the accusative:

• fundur = a meeting, meeting (nominative)
• fund = a meeting (accusative, indefinite)
• fundinn = the meeting (accusative, definite)

So Ég skrifa fundinn... means I write the meeting... / I enter the meeting...

Dagatalið mitt is the most normal everyday way to say my calendar in Icelandic.

A very common Icelandic pattern is:

• noun + definite article + possessive

So:

• dagatalið mitt = my calendar
• bíllinn minn = my car
• húsið okkar = our house

Mitt dagatal is possible, but it sounds more emphatic, contrastive, or stylistically marked, as if you are stressing my calendar rather than someone else’s.

Because dagatal is a neuter noun, and the possessive must agree with it in gender, number, and case.

Here:

• dagatal = neuter singular
• accusative singular neuter possessive = mitt

So:

• masculine: minn
• feminine: mín
• neuter: mitt

That is why you get dagatalið mitt.

Because í can take either accusative or dative, depending on the meaning:

• accusative = motion/direction, roughly into
• dative = location, roughly in

In this sentence, the idea is:

• writing the meeting into the calendar
• putting a reminder into the phone

So accusative is used:

• í dagatalið mitt
• í símann

Compare:

• Fundurinn er í dagatalinu mínu = The meeting is in my calendar. (location → dative)
• Áminningin er í símanum = The reminder is in the phone. (location → dative)

Because set is the 1st person singular present tense of setja.

The verb goes like this in the present:

• ég set = I put/set
• þú setur = you put/set
• hann/hún/það setur = he/she/it puts/sets

So with ég, the correct form is set.

That is very common in Icelandic. For many verbs, the infinitive and the 1st person singular present look the same.

So:

• að skrifa = to write
• ég skrifa = I write

But other persons are different:

• þú skrifar
• hann skrifar

So the ég tells you that skrifa here is a finite verb, not an infinitive.

Because Icelandic, like English, often leaves out a repeated subject in coordinated clauses when it is the same subject.

So:

• Ég skrifa fundinn í dagatalið mitt og set líka áminningu í símann.

means:

• I write the meeting in my calendar and also set a reminder in my phone.

You could say og ég set líka..., but it is not necessary.

That is a very natural position for líka in a neutral sentence.

Here:

• set líka áminningu = also set a reminder

The placement of líka can shift the emphasis a little. For example:

• Ég skrifa líka fundinn... = I also write the meeting...
• Ég set líka áminningu... = I also set a reminder...
• Ég set áminningu líka... = I set a reminder too

So the given version is a normal, neutral way to say it.

Because Icelandic often leaves out possessives when the owner is obvious from context.

In a sentence like this, listeners will naturally assume it means my phone. So:

• í símann often effectively means into my phone here

If you want to stress it, you can add the possessive:

• í símann minn = into my phone

That would be more likely if you were contrasting it with someone else’s phone.

Because it means a reminder, not the reminder.

• áminningu = a reminder (accusative singular, indefinite)
• áminninguna = the reminder (accusative singular, definite)

In this sentence, the speaker is introducing a reminder as a new thing, so the indefinite form is natural.

Yes, it is understandable and natural enough. It means something like write the meeting into the calendar or put the meeting in the calendar.

English usually prefers:

• put the meeting in my calendar
• write the meeting down in my calendar

Icelandic can also use other verbs here, especially:

• skrá fundinn í dagatalið = enter/register the meeting in the calendar

So skrifa works, but skrá is also very common in this kind of context.

They are:

• fundur — masculine
• dagatal — neuter
• áminning — feminine
• sími — masculine

Knowing the gender helps you understand forms like:

• fundinn
• dagatalið
• áminningu
• símann
• mitt

because Icelandic endings depend heavily on gender, number, definiteness, and case.