Ég svara tölvupóstinum eftir morgunmat.

Because ég takes the 1st person singular form of the verb.

The verb is að svara = to answer / to reply.

Present tense:

• ég svara = I answer
• þú svarar = you answer
• hann/hún/það svarar = he/she/it answers

So svara is the correct form with ég.

It can be either, depending on context.

Ég svara tölvupóstinum eftir morgunmat can mean:

• I answer the email after breakfast (habitual / general)
• I’m answering the email after breakfast
• I’ll answer the email after breakfast (future sense)

Icelandic often uses the present tense where English might use either present or future.

If you want to make the future more explicit, you can say:

• Ég mun svara tölvupóstinum eftir morgunmat.

Because the verb að svara takes a dative object in Icelandic.

The dictionary form is:

• tölvupóstur = email

But after svara, you need the dative:

• tölvupósti = to/an email, email (dative singular, indefinite)
• tölvupóstinum = the email (dative singular, definite)

So the sentence uses tölvupóstinum because:

1. svara requires the dative
2. the noun is definite: the email

Not in the way you would normally translate the sentence into English.

Even though the noun is in the dative, the natural English translation is still:

• the email or
• to the email only if you are translating the grammar very literally

This is a common difference between Icelandic and English:

• English often says answer the email or reply to the email
• Icelandic says svara
  • dative noun

So the case is important grammatically, but you do not always translate it with an English preposition.

It shows that the noun is:

• singular
• definite (the)
• dative
• masculine

A very important Icelandic feature is that the definite article is usually attached to the end of the noun, instead of being a separate word.

So instead of a separate word like English the, Icelandic often adds an ending.

Here:

• tölvupóstur = email
• tölvupóstinum = the email (in the dative singular)

Because morgunmat here means breakfast in a general sense, just like English after breakfast.

In Icelandic, meals are often used without the definite article when speaking generally:

• eftir morgunmat = after breakfast
• eftir hádegismat = after lunch
• eftir kvöldmat = after dinner

If you meant a specific breakfast, you could use the definite form:

• eftir morgunmatinn = after the breakfast

But in ordinary usage, eftir morgunmat is the natural choice.

Here eftir takes the dative because it means after in a temporal sense.

So in:

• eftir morgunmat

the noun after eftir is in the dative.

That is why you do not see the dictionary form morgunmatur here.

Because morgunmatur is the nominative form, the form you usually find in a dictionary.

In this sentence, the noun comes after eftir, which requires the dative here. So the form changes:

• morgunmatur = breakfast (nominative)
• morgunmat = breakfast (dative here)

For this noun, the dative form happens to look shorter and does not keep the -ur ending.

Yes.

You can say:

• Eftir morgunmat svara ég tölvupóstinum.

That is perfectly natural.

But notice what happens: Icelandic is a verb-second language in main clauses. That means the finite verb usually stays in the second position.

So when Eftir morgunmat comes first, the verb svara comes next, and ég moves after the verb:

• Eftir morgunmat svara ég tölvupóstinum.

You would not normally say:

• Eftir morgunmat ég svara tölvupóstinum.

Yes. Icelandic very often forms new words by combining smaller words into one compound word.

For example:

• morgun + matur → morgunmatur = breakfast
• tölva + póstur → tölvupóstur = email

This is extremely common in Icelandic. Where English may use:

• two separate words
• a hyphen
• or a phrase

Icelandic often prefers a single compound word.

That is why long words are so common in Icelandic.