Hún vill ekki sleppa kennslustundinni, jafnvel þótt hún sé þreytt eftir vinnu.

Vill is the 3rd person singular present form of vilja (to want).

Because the subject is hún (she), Icelandic uses:

• ég vil = I want
• þú vilt = you want
• hún vill = she wants

So Hún vill means she wants.

In a normal Icelandic main clause, the finite verb usually comes early in the sentence, and ekki (not) normally comes after that verb.

So:

• Hún vill ekki ... = She does not want ...

This is different from English, where we use do not before the main verb.

Here sleppa means to skip or not attend something.

So sleppa kennslustundinni means skip the lesson/class.

This verb can also mean other things in other contexts, such as let go, so learners often need to rely on context.

A very useful distinction is:

• sleppa e-u = skip something, often more voluntary
• missa af e-u = miss something, often unintentionally

So this sentence suggests she doesn’t want to skip the class, even though she is tired. It sounds more like a choice than an accident.

Because sleppa takes the dative case, and the noun is also definite.

So:

• kennslustund = lesson / class
• kennslustundinni = the lesson / the class, in the dative singular

The ending -inni shows both:

• definite article = the
• dative singular form

Jafnvel þótt means even though or even if, depending on context.

In this sentence, it works like even though:

• jafnvel þótt hún sé þreytt = even though she is tired

It introduces a contrast: she is tired, but she still does not want to skip the class.

Sé is the subjunctive form of vera (to be).
Er is the normal indicative form.

After conjunctions like þótt or jafnvel þótt, Icelandic very often uses the subjunctive:

• þótt hún sé þreytt = though she be / even though she is tired

For learners, the important point is: after þótt, subjunctive is very common and often expected.

Because this is a subordinate clause introduced by jafnvel þótt.

In Icelandic:

• main clauses often follow verb-second word order
• subordinate clauses usually do not

So after jafnvel þótt, the normal order is:

• conjunction + subject + verb

That gives:

• jafnvel þótt hún sé þreytt

Þreytt is agreeing with hún (she).

After vera (to be), Icelandic predicate adjectives agree with the subject in gender, number, and usually case. Here the subject is:

• feminine
• singular
• nominative

So the correct form is þreytt.

For comparison:

• hann er þreyttur = he is tired
• hún er þreytt = she is tired

Here eftir vinnu means after work in a general sense, so Icelandic does not need the definite article.

The noun vinna is in the dative singular here after eftir in this time expression.

So:

• eftir vinnu = after work
• eftir vinnunni would mean something more like after the work / after the job, depending on context

Yes, often you can.

For example:

• Hún vill ekki sleppa kennslustundinni, þó að hún sé þreytt eftir vinnu.

That is also natural.
Jafnvel þótt can sound a bit stronger, more like even though rather than just though/although.

Because the second part is a subordinate clause.

Icelandic commonly separates this kind of clause with a comma:

• main clause: Hún vill ekki sleppa kennslustundinni
• subordinate clause: jafnvel þótt hún sé þreytt eftir vinnu

So the comma helps show the structure clearly.

Two tricky sounds here are:

• þ in þótt: pronounced like th in thin
• ll in vill: in Icelandic this is often not a simple English l sound; it is commonly pronounced more like a tl-like sound

Very roughly:

• vill sounds something like vitl
• þótt starts with the th of thin

The exact pronunciation depends a bit on accent, but those approximations are useful for learners.