Ég nota aðganginn að gagnagrunninum og opna rafbókina.

In Icelandic, the definite article is usually attached to the end of the noun, not written as a separate word.

So here:

• aðganginn = the access
• gagnagrunninum = the database
• rafbókina = the e-book

That is why you do not see a separate word for the.

A rough breakdown is:

• aðgang-inn = access + the
• gagnagrunn-inum = database + the
• rafbók-ina = e-book + the

The exact ending changes depending on gender, number, and case.

Because aðganginn is the accusative singular definite form of aðgangur.

The noun’s basic form is:

• aðgangur = access

But after the verb nota (to use), the direct object normally goes in the accusative. So:

• nominative: aðgangurinn = the access
• accusative: aðganginn = the access

In this sentence, aðganginn is the thing being used, so accusative is needed.

So the logic is:

• Ég nota ... = I use ...
• what do I use? aðganginn

Here, að is a preposition meaning something like to.

It is not the infinitive marker here.

So:

• aðgangur að einhverju = access to something

That means:

• aðganginn að gagnagrunninum = the access to the database

This is a fixed pattern you should learn as a unit:

• aðgangur að + dative

So if you learn the noun aðgangur, it is very useful to learn it together with the preposition it commonly takes:

• aðgangur að einhverju = access to something

Because gagnagrunninum is in the dative singular definite.

There are two reasons for that:

1. The noun phrase depends on aðgangur að ...
2. The preposition að here takes the dative

The dictionary form is:

• gagnagrunnur = database

But in this sentence you need:

• gagnagrunninum = the database in dative singular definite

So the full phrase is:

• aðgangur að gagnagrunninum = access to the database

This is a very common thing in Icelandic: a noun or preposition can force another noun into a certain case.

They do look like infinitives, and in these verbs the 1st person singular present happens to be the same as the infinitive.

So:

• að nota = to use
• ég nota = I use

and

• að opna = to open
• ég opna = I open

This is normal for many Icelandic weak verbs.

Other persons look different, for example:

• ég nota = I use
• þú notar = you use
• hann/hún/það notar = he/she/it uses

and

• ég opna = I open
• þú opnar = you open
• hann/hún/það opnar = he/she/it opens

So even though nota and opna look like infinitives, here they are finite verbs because the subject ég shows that they mean I use and I open.

Because rafbókina is the accusative singular definite form of rafbók.

The basic form is:

• rafbók = e-book

Since opna takes a direct object, and direct objects are commonly in the accusative, you get:

• nominative: rafbókin = the e-book
• accusative: rafbókina = the e-book

So in:

• opna rafbókina

the word rafbókina is the thing being opened.

Also notice that rafbók is a feminine noun, and that affects the ending.

No. It is perfectly normal to say:

• Ég nota aðganginn að gagnagrunninum og opna rafbókina.

The subject ég applies to both verbs:

• Ég nota ...
• (ég) opna ...

This works just like English:

• I use the database access and open the e-book.

You could repeat ég for emphasis or clarity in some contexts, but it is not necessary here.

No, this is a very straightforward Icelandic sentence.

It follows a simple pattern:

• Ég = subject
• nota = verb
• aðganginn að gagnagrunninum = object
• og = and
• opna = second verb
• rafbókina = object

So the structure is basically:

• Subject + Verb + Object + and + Verb + Object

That is very natural.

One thing to know about Icelandic in general is that it often follows a verb-second pattern in main clauses. But since the sentence begins with the subject Ég, the verb naturally comes right after it, so the word order looks very similar to English here.

A good way is to ask what each word is doing in the sentence.

1. aðganginn

This is the direct object of nota:

• Ég nota hvað?
  aðganginn

So it is in the accusative.

2. gagnagrunninum

This comes after að in the phrase:

• aðgangur að einhverju

That pattern requires the dative, so you get gagnagrunninum.

3. rafbókina

This is the direct object of opna:

• Ég opna hvað?
  rafbókina

So it is also in the accusative.

So the sentence contains:

• accusative: aðganginn
• dative: gagnagrunninum
• accusative: rafbókina

This is very typical Icelandic: the verb or preposition often tells you which case is needed.

No. að is a very common Icelandic word with more than one use.

For example, it can be:

• an infinitive marker:
  að lesa = to read
• a preposition:
  að húsinu = to the house / at the house, depending on context

In your sentence, it is definitely a preposition, because it belongs to the phrase:

• aðgangur að ... = access to ...

So here it does not mean the same kind of to as in to open or to use. It is part of the noun phrase access to the database.