Hvernig sem veðrið er, kemur hún alltaf í kennslustundina.

Together, hvernig sem introduces a concessive idea: however ... or no matter how ....

So Hvernig sem veðrið er means no matter what the weather is like. Even though hvernig by itself usually means how, the whole expression is idiomatic and should be understood as one pattern.

Here, sem is part of a very common Icelandic pattern:

• hver sem = whoever
• hvar sem = wherever
• hvenær sem = whenever
• hvernig sem = however / no matter how

So sem helps turn the question word into a free-choice or concessive expression.

Veðrið is the definite form of veður, so it means the weather.

That is the normal way to talk about weather in Icelandic, just as English also usually says the weather rather than just weather in this kind of sentence. Grammatically, veðrið is also the subject of er.

It is the nominative singular definite form of the neuter noun veður.

You can break it down like this:

• veður = weather
• veðrið = the weather

The ending -ið is the definite article attached to the noun.

Er is the 3rd person singular present tense of vera = to be.

It agrees with veðrið, which is singular. Icelandic present-tense verb forms do not change for gender, so neuter singular still takes er just like masculine or feminine singular subjects would.

This is because Icelandic follows the V2 rule in main clauses: the finite verb normally comes in the second position.

The first position here is already taken by the whole introductory clause:

Hvernig sem veðrið er

So the finite verb of the main clause, kemur, must come next:

Hvernig sem veðrið er, kemur hún alltaf í kennslustundina.

Without that fronted clause, the neutral order would be:

Hún kemur alltaf í kennslustundina.

In a neutral main clause, adverbs like alltaf often come after the subject.

So after the V2 order puts kemur first, the subject hún follows, and then alltaf:

kemur hún alltaf

This is a very natural word order. In a simple clause with no fronting, you would also get:

Hún kemur alltaf í kennslustundina.

It is accusative singular definite of the feminine noun kennslustund.

The main forms are:

• kennslustund = a lesson / class
• kennslustundin = the lesson / the class
• kennslustundina = the lesson / the class, in the accusative
• kennslustundinni = in/to the lesson / the class, in the dative definite form when needed

In this sentence, the accusative is required by the preposition í because the meaning is directional.

Because í takes different cases depending on meaning:

• accusative for motion toward / into
• dative for location / being in

Here she is coming to the class, so the phrase is directional:

í kennslustundina

Compare:

• Hún kemur í kennslustundina. = She comes to the class.
• Hún er í kennslustundinni. = She is in the class.

In Icelandic, the definite form often sounds natural when referring to a specific scheduled lesson or class session.

So í kennslustundina suggests to the class/the lesson in question. English often uses a more article-less expression like to class, but Icelandic does not always match English article usage directly.

It can suggest both, depending on context.

Literally, koma means to come. But in a sentence about classes, hún kemur alltaf í kennslustundina very naturally implies she always shows up for class or she always attends the lesson.

So the verb keeps its basic meaning, but the overall sentence can be understood more idiomatically.

Yes. You could also say:

Hún kemur alltaf í kennslustundina, hvernig sem veðrið er.

That keeps basically the same meaning, but the emphasis changes a little. The original version foregrounds the concessive idea first: whatever the weather is like...

Yes, it is normal here.

The comma separates the introductory subordinate clause:

Hvernig sem veðrið er

from the main clause:

kemur hún alltaf í kennslustundina

This makes the structure easier to read and shows clearly where the main statement begins.