Hvar sem hún situr í kennslustofunni, sér hún töfluna vel.

Hvar sem means wherever or no matter where.

It is made from:

• hvar = where
• sem = a small connecting word that often helps create meanings like whoever, whatever, wherever, etc.

So Hvar sem hún situr ... means something like Wherever she sits ...

This is because of Icelandic V2 word order in main clauses.

In the sentence:

• Hvar sem hún situr í kennslustofunni = subordinate clause
• sér hún töfluna vel = main clause

In the main clause, the finite verb usually comes in the second position. Since the whole first clause comes first, the verb sér has to come before the subject hún:

• Hvar sem hún situr í kennslustofunni, sér hún töfluna vel.

But inside the first clause, Icelandic does not use that same main-clause V2 pattern, so normal subject + verb order appears:

• hún situr

So this contrast is completely normal.

Here, sér is the verb.

It is the 3rd person singular present form of sjá (to see):

• ég sé = I see
• þú sérð = you see
• hún sér = she sees

You can tell it is a verb here because it has:

• a subject: hún
• an object: töfluna

There is also a pronoun sér in Icelandic, but that is a different word entirely.

Because it comes after í, and here í means in in the sense of location, not movement.

With í:

• dative is used for location: in
• accusative is used for motion into something: into

So:

• í kennslustofunni = in the classroom → location → dative
• í kennslustofuna = into the classroom → movement → accusative

Also, kennslustofunni includes the definite article:

• kennslustofa = classroom
• kennslustofunni = in the classroom

The dictionary form is kennslustofa.

It is a feminine noun meaning classroom.

Very roughly, the form breaks down like this:

• kennslustofa = classroom
• kennslustofunni = the classroom in the dative singular

So the ending changes because of both:

• case: dative
• definiteness: the

Because töfluna is the direct object of sér, and sjá takes the accusative.

So:

• tafla = a board
• töfluna = the board, in the accusative singular

This change is normal noun inflection.

In this sentence, töfluna means the board.

No. In this context, tafla means board, such as a classroom board.

So töfluna here means:

• the board
• often naturally translated as the blackboard or the whiteboard, depending on context

A learner might guess table because it looks similar to English words like table, but that is not the meaning here.

Because vel is an adverb, and it modifies the verb sér.

• vel = well
• sér ... vel = sees ... well

English does the same thing:

• She sees the board well

An adjective would not fit here, because the sentence is describing how she sees, not describing the board itself.

Because each clause needs its own subject.

Even though it is the same person in both parts, Icelandic normally says:

• hún situr
• hún sér

So the subject is stated again in the main clause. That is the normal, natural way to say it.

The comma marks the boundary between the introductory subordinate clause and the main clause:

• Hvar sem hún situr í kennslustofunni,
• sér hún töfluna vel.

It helps show that the first part sets up the condition or circumstance, and the second part gives the main statement.

Literally, it means she sees the board well.

But in natural English, it is often better translated as:

• she can see the board well

That is because English often uses can where Icelandic simply uses the ordinary present tense.

So both ideas are connected, but the Icelandic sentence itself does not contain a separate word for can.

Yes. This is a very useful pattern in Icelandic.

For example:

• hver sem = whoever
• hvað sem = whatever
• hvenær sem = whenever
• hvernig sem = however
• hvar sem = wherever

So this sentence shows a pattern that you can reuse in many other sentences.