Ég tek skelina upp úr töskunni.

Because tek is the conjugated present-tense form of the verb taka for ég.

• taka = the infinitive, to take
• ég tek = I take
• þú tekur = you take
• hann/hún/það tekur = he/she/it takes

So Icelandic changes the verb form depending on the subject, much more than English usually does.

Yes. Icelandic often uses the simple present where English might use either the simple present or the present continuous.

So Ég tek skelina upp úr töskunni can mean something like:

• I take the shell out of the bag
• I am taking the shell out of the bag

The exact feel depends on context.

Here, úr is the preposition that means out of / from inside.
The word upp is a particle that often goes with verbs like taka in expressions of removing or lifting something out.

So:

• úr töskunni = out of the bag
• taka ... upp úr ... = take ... out of ...

In natural English, you usually would not translate upp separately. It is part of the Icelandic expression.

That is normal in Icelandic. Verb particles such as upp do not always stay right next to the verb.

Here the structure is:

• Ég tek = I take
• skelina = the object
• upp úr töskunni = the rest of the phrase

This is a bit like English phrasal verbs, where you can say:

• take out the shell
• take the shell out

So taka skelina upp is a natural Icelandic pattern.

Because it is:

• the noun skel = shell
• in the accusative singular
• with the definite article attached, so it means the shell

It is in the accusative because it is the direct object of tek.

A rough breakdown is:

• skel = shell
• skelina = the shell

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

Because úr requires the dative case, so taska has to appear in the dative singular definite form.

• base noun: taska = bag
• dative singular: tösku
• dative singular definite: töskunni = the bag after a dative-governing preposition

So úr töskunni means out of the bag.

That is a normal vowel change in Icelandic declension. Some nouns change their stem vowel in oblique cases.

For taska, the pattern is roughly:

• nominative: taska
• accusative/dative/genitive forms: tösku-

Then the definite ending is added, giving töskunni in this sentence.

So this is not a different word; it is just the same noun in a different grammatical form.

There are three important case roles here:

• Ég is nominative because it is the subject
• skelina is accusative because it is the direct object of taka
• töskunni is dative because úr takes the dative

So the sentence is a good example of how Icelandic marks grammatical roles with case endings.

Yes, that is possible, and it would still be understood as I take the shell out of the bag.

However, taka ... upp úr ... is a very natural and common way to express physically taking something out. The upp makes the action feel a bit more complete or idiomatic.

So:

• Ég tek skelina úr töskunni = understandable and fine
• Ég tek skelina upp úr töskunni = very natural for take the shell out of the bag

Because in Icelandic, the definite article is usually attached to the noun itself.

So instead of a separate word like English the, Icelandic normally uses endings:

• skelina = the shell
• töskunni = the bag in the dative

There is also a separate definite form (hinn / hin / hið), but that is not the normal everyday way to say the in a simple sentence like this.