Ég hef ekki mikla matarlyst í dag, en ég get samt borðað eina pylsu.

Because in a normal Icelandic main clause, the finite verb usually comes early, in the typical V2 pattern. With the subject first, the order is:

subject + finite verb + ekki / adverb + rest

So:

Ég hef ekki mikla matarlyst ...
= I have not much appetite ...

If you moved something else to the front, the verb would still stay in second position:

Í dag hef ég ekki mikla matarlyst.
= Today I don’t have much appetite.

Because matarlyst is a feminine singular noun, and here it is the direct object of hafa (to have), so it is in the accusative.

The adjective mikill (much / great) has to agree with the noun in gender, number, and case:

• nominative feminine singular: mikil
• accusative feminine singular: mikla

So:

• mikil matarlyst = nominative
• mikla matarlyst = accusative

Here you need the accusative form: mikla.

No. The negation does not change the case here.

It is accusative because hafa takes a direct object in the accusative:

• Ég hef matarlyst.
• Ég hef ekki matarlyst.

In both cases, the object is still the object of hafa.

Matarlyst means appetite.

It is a compound word:

• matar- = from matur (food)
• lyst = desire / appetite / liking

So literally it is something like food-desire, but the natural English meaning is appetite.

Í dag means today.

Literally it is in day, but as a phrase it simply means today. The form dag is the accusative of dagur (day).

For a beginner, the best approach is to learn í dag as a fixed expression.

Here samt means still, anyway, or nevertheless.

So:

en ég get samt borðað eina pylsu
means something like:

• but I can still eat one hot dog
• but I can eat one hot dog anyway

It adds the idea of despite that.

That is a natural place for it in Icelandic word order.

In the clause:

ég get samt borðað eina pylsu

the finite verb is get, and short adverbs like samt often come right after the finite verb.

So the structure is:

subject + finite verb + adverb + main verb form + object

Because en (but) joins a new clause, and that clause normally has its own subject.

So Icelandic says:

Ég hef ekki mikla matarlyst í dag, en ég get samt borðað eina pylsu.

This is very similar to English:

I don’t have much appetite today, but I can still eat one hot dog.

This is a very common learner question.

After geta (can / be able to), Icelandic commonly uses the verb form called sagnbót. For borða, that form is borðað.

So:

• borða = infinitive, to eat
• borðað = the form used here after get

That means:

ég get borðað = I can eat

Even though borðað may look like a past-participle-type form to an English speaker, here it does not mean eaten. It is just the normal form used in this construction.

Because geta does not take að before the following verb in this kind of sentence.

So you say:

• Ég get borðað. = I can eat.

not:

• Ég get að borðað.

For English speakers, this is one of those patterns best learned as a set phrase.

Because pylsa is a feminine noun, and here it is the direct object of borða, so it is in the accusative singular:

• nominative: pylsa
• accusative: pylsu

The word einn (one) must agree with it:

• feminine accusative singular: eina

So:

eina pylsu = one hot dog / one sausage

It can do both jobs, depending on context.

Icelandic does not have a normal indefinite article like English a/an, so einn/ein/eitt can sometimes feel article-like.

Here eina pylsu most naturally means:

• one hot dog
• or a single hot dog

It gives a slightly more specific feeling than just pylsu.

Yes, you could.

• Ég get samt borðað pylsu.

That would still be understandable, and it would mean something like I can still eat a hot dog / some sausage depending on context.

But eina pylsu is more precise and emphasizes one.

Both are possible, but in Icelandic everyday usage pylsa very often means hot dog, especially in food contexts like this one.

So in this sentence, one hot dog is probably the most natural translation.