Ég dreg stólinn að borðinu.

Draga is the infinitive, meaning to pull / to drag.
In the sentence, the verb is conjugated for I in the present tense:

• ég dreg = I pull / I drag
• að draga = to pull / to drag

So Ég dreg stólinn að borðinu uses the correct finite verb form for ég.

This verb is a bit irregular-looking because the vowel changes:

• infinitive: draga
• present, 1st person singular: dreg

That kind of stem change is normal in Icelandic.

Here is the breakdown:

• Ég = I
  
  • subject, nominative case
• dreg = pull / drag
  
  • present tense verb
• stólinn = the chair
  
  • direct object, accusative case
• að = to / up to / toward
  • preposition
• borðinu = the table
  • object of the preposition, in the dative case

So the structure is basically:

I + pull + the chair + toward/up to the table

Because stólinn means the chair, while stóll means just a chair / chair.

Icelandic usually adds the definite article onto the end of the noun instead of using a separate word like English the.

So:

• stóll = chair
• stólinn = the chair

Also, in this sentence the noun is the direct object, so it appears in the accusative singular form:

• nominative: stóll
• accusative: stól
• accusative definite: stólinn

Because the preposition að takes the dative case.

The noun borð means table, and its definite singular forms include:

• nominative/accusative definite: borðið = the table
• dative definite: borðinu

Since the sentence uses að borðinu, Icelandic requires the dative:

• að borðinu = to / up to / toward the table

So this is not just a different article form; it is a case change caused by the preposition.

No. Að is a very common Icelandic word with several uses.

In this sentence, að is a preposition meaning something like:

• to
• toward
• up to

But að can also be used in other ways, for example:

• as the infinitive marker: að lesa = to read
• in various fixed expressions
• with different shades of meaning depending on context

So here you should understand að specifically as a preposition governing the dative.

Because að and til do not mean exactly the same thing.

In a sentence like this, að borðinu suggests movement up to or toward the table, often with the idea of bringing the chair near it.

• Ég dreg stólinn að borðinu = I pull the chair up to the table

Using til would sound different. Til often means to, toward, or as far as, but it is not the usual choice when you mean moving something into position next to another object in this way.

So að borðinu is the natural phrasing for pull the chair up to the table.

Stólinn is in the accusative singular definite.

That is because it is the direct object of the verb dreg.
The action is being done to the chair:

• I pull the chair

Many Icelandic verbs, including draga, take a direct object in the accusative.

So:

• subject: ég nominative
• object: stólinn accusative

Yes. This is very normal Icelandic word order:

• Ég = subject
• dreg = verb
• stólinn = direct object
• að borðinu = prepositional phrase

So it follows a familiar pattern:

Subject + Verb + Object + Prepositional Phrase

Icelandic word order can be more flexible than English in some contexts, but this sentence is straightforward and natural.

Yes, but the meaning changes.

• Ég dreg stólinn að borðinu = I pull the chair up to the table
• Ég dreg stól að borði = I pull a chair up to a table

Without the definite endings, the nouns are indefinite. That makes the sentence more general or less specific.

So the version with -inn and -inu is used when both objects are understood as specific: the chair and the table.

It can suggest either, depending on context, but here it most naturally means up to the table.

That is, the chair ends up near the table, in contact with it or in its proper position next to it.

So a very natural English sense would be:

• I pull the chair up to the table

That is often a better match than a bare to the table, because English up to captures the physical positioning nicely.

A few useful notes:

• Ég: the é is like ye at the start, so roughly yeg
• dreg: the g at the end is not pronounced like a strong English g in go; Icelandic final consonants can sound softer than English learners expect
• stólinn: the ó is a long o sound; the ending -inn is pronounced clearly
• borðinu: ð is like the th in this, not thin

A rough beginner-friendly approximation might be:

• Ég dreg stólinn að borðinu
• yeg drehg STOH-lin ath BOR-thi-nu

That is only approximate, but it can help at first.

The dictionary forms are:

• stóll = chair
• borð = table

In the sentence, they appear in inflected forms:

• stólinn = from stóll
• borðinu = from borð

This is very important in Icelandic: the form you see in a sentence is often not the dictionary form, because nouns change for:

• case
• number
• definiteness

So learners should get used to recognizing nouns in changed forms, not just in their base form.