Ég er alltaf tilbúinn þegar kennslustundin hefst.

Yes:

• Ég = I
• er = am
• alltaf = always
• tilbúinn = ready
• þegar = when
• kennslustundin = the lesson / the class period
• hefst = begins / starts

So the structure is basically:

I am always ready when the lesson begins.

Tilbúinn is an adjective meaning ready, and it has to agree with the person being described.

Here, the speaker is ég (I), so the adjective matches the speaker in gender, number, and case.

• a male speaker: Ég er alltaf tilbúinn
• a female speaker: Ég er alltaf tilbúin

Also, after vera (to be), Icelandic normally uses the strong adjective form in predicate position, which is why you get tilbúinn, not a weak form.

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word.

So:

• kennslustund = lesson / class period
• kennslustundin = the lesson / the class period

That final -in is the attached definite article here.

Also, kennslustund is a compound noun:

• kennsla = teaching / instruction
• stund = period / hour / session

So the whole word means something like teaching session, i.e. lesson.

Hefst is the 3rd person singular present form, meaning begins or starts here.

It matches kennslustundin, which is singular:

• kennslustundin hefst = the lesson begins

The dictionary form is hefjast. This verb is often used for something beginning.

So:

• hefst = begins
• hófst = began
• hafist = a subjunctive form you may meet later

Because þegar introduces a subordinate clause.

In main clauses, Icelandic usually follows a verb-second pattern. But in subordinate clauses, the most normal order is subject + verb.

So this is the standard order:

• þegar kennslustundin hefst

not usually:

• þegar hefst kennslustundin

So after þegar, the clause behaves more like:

• when the lesson begins

with the lesson first, then begins.

Here, þegar means when.

But yes, þegar can also mean already in other contexts.

For example:

• Ég kem þegar. = I’m coming right away / already coming soon depending on context
• Þegar hann kom, fór ég. = When he came, I left

So þegar is one of those Icelandic words whose meaning depends on how it is used in the sentence. In your sentence, because it introduces a clause with a verb, it clearly means when.

That is the most natural placement for this kind of adverb in a simple sentence.

So Icelandic normally says:

• Ég er alltaf tilbúinn

Here the order is:

• subject: Ég
• verb: er
• adverb: alltaf
• adjective/predicate: tilbúinn

You may see other word orders for emphasis, but this is the neutral everyday one.

You probably could be understood, but it sounds less natural in ordinary Icelandic.

The usual order is:

• Ég er alltaf tilbúinn

Putting alltaf later can sound marked or unnatural unless there is a special emphasis.

So as a learner, the safest choice is to keep alltaf before the adjective here.

Yes:

• Þegar kennslustundin hefst er ég alltaf tilbúinn.

That is perfectly natural.

But notice what happens in the main clause after the fronted subordinate clause:

• er ég instead of ég er

That is because Icelandic main clauses still want the finite verb early in the sentence. So fronting the þegar clause changes the word order of the main clause.

Yes, in many situations you can.

• kennslustundin hefst
• kennslustundin byrjar

Both can mean the lesson begins / starts.

A useful rule of thumb:

• byrjar is often a bit more everyday and conversational
• hefst can sound a bit more formal or written

But both are correct, and both are common enough to recognize.

It is in the nominative case, because it is the subject of hefst.

In the clause:

• kennslustundin hefst

the thing doing the beginning is the lesson, so kennslustundin is the subject, and subjects are usually nominative in Icelandic.

That is why you see the nominative definite form kennslustundin here.